Bac Complexes3imbac lak

حصریا كتاب العمالق لألستاذ الفاضل بواب نور الدین

جزء األعداد المركبة من البكالوریا

زوروا موقعنا

منتدى وھران

www.mat

hsac

adem

y.net

-L as IEtLr.tr?!5-Y r'

-C u;tv*lCO] r.rri ''a

ajrar t e

. C a.u r.r'r [ra] orx "o

avr.ul t+

[r'en]z'rral ;t" 1t

e æg(z - | = -L, * Zn t Ass.- 4,- z ;.Ë')Ltl ùls !n'Jt :"e"o" O

'sak eZ

.Izt^;*sçrlBD],orL,,:l apu U-i 1T

'('BD )ç:c''rr t v

.B zt xtslrrb D 'i..1e

B è3r-. éir ]BD)e'Ài*!l ' à'-r (r'

. D t B W}lij/t heb ['BD ] 'ArLe etl ôrilû'l ( ù

tJ)l(v) cP az-'Jr 4çYlO

i|51,9i1 g'].rle 0 a:r-9 6 e M oQ )of.;o 6.rJl ùr.rs'r! afr[l'at$tt:-rS ;S

z' - z,t - eis (z - z o),çÊ tt'(z)asat:t u(")*:It

zr - z,q - "'3 (", -ze),JF *s

;n t+^lz,zE =e'l {zo -zo)+ zn=...-t+)tJ (t-i )'o-e

6l E e'Uz;Sl eaI lu'-elig A ofv 9r,l ùb9Jb D ;L:.t| ô19e :i!!t ,-^8.t -'-1" (l-i ),trii-v

'. (") -9 (i) bô Ûbo,.*.â'l .irau. yt lB

l- - l-1 . 'r I 'lto -oDt-t; -z,tl;*glz +tl-lz -ll:l4r

'[Aa]a;Uill rr*. ÈoMaa;.itacsn5'c!!à *sDM -AM 'r!tt!bs

'" :: rst^{| ùitfB C ] I [Z o ] a:'eas JF et'. A B CD *rt'31 ai trj

www.mat

hsac

adem

y.net

æelz +il=lz -rl+,.[n c ] -,"*ztt ç*s|lnlæa,/

(9) *e @,,all ,ôr-.VO

Z-Zt -'l,Lâû lôrr::É ù9q ei.*r z aÀ,y)t ûts M L:,4 ic*re :JJ )j4-zB.B eaa,i/| rr" b [lB ]r.,rra s:lt ôjt.rJt 9o 4a

z +i _z - zp 4r,$

z+1 z-Zclir, t4aô tfi"-tùÉ eiFt z zÀ,y)t cls M b;ult ire,cq.o:!i!

.C at at l.rr.[CD]r".,.,1-a eil ôitJ' .,À

,+ti 4r?,.b

:ohs r.!ye *'=+;jfrZ. - Z/-

(, -- \ -@rcl":= l-!+ktt (r en) ! z - zo

=s\.

_"C ) - z_Zc

- -+ +t(CM ;DM )-zr+kn (f en) 1s112 *Zç!z =zD)tl,,s

tù tffit sl (tutic iM -f ):9i

(cM.DM =0)gi (M+ciM _D),,4

srl ôjf{rt,? ù. ffi =0 e*- çs:*tr e M .t t;starr.9.. ;l pt*ie

.[co]",l"ert$zfill* ;se e.'.r. z eÂ'r!r| .3l'r M J^âjJl &g,cac :!5J

. C aLr:sl lart" [CD ] r^,.,râ sJt ôrltrJt ,,o

.+fr-rrl éJarl tlo*.rL 6rbd o.ô d! Js,ââil ùq

www.mat

hsac

adem

y.net

nc(z -t)-*(ru -6tffi1=-5+2k1r,o,?æc(z -t)=-![zn],

. B alo;;sl tJrt D lih

tlBD) es

G;tM'îPd' t-1--

\_--------.(o, ilû *,,+.r*rl e

t+, t';=- - i.:.'..Y I.+ -+-zr)-(i;BM) +?*r,ii.l

r"- arg(z - i ) - -f + 2k n,a;,

C.!' Z ai'Yjl otS M,haft &,ensr :6,

4s B oi*" çiJl I ÀD) iqii{.,.U \Â.

aÀf ÈÂ:-ff \i ^l sà MLilt Are.44

@@rJ r"brll firll gl! u. 9*:,o :lru ,99:-Ât

a Zæll4b.yl .*|1 h. eJb,JS é.i{s

û

,9

!!

IJ

)

(+ (v ti

/) a-'L- Zt 2-i r-2iiJ,rG,cJJ .P r=Jrll o.rrJl O

,*(t+i )z -3+i -o

s.ô..ôr ùJt

+L,

/sr.,."Gvo

tjniir ù.lt

!at9.

IsZ rtL-st".=-(r uc Zg O.cJ ôJ.,

,9o zo2olo.JrUs*Jl

'lZe'+ Jze-'4 Jze'q-érfl .s.r;ll ayY q|Élt G)

:!*-l+I

' . I lf,lio'T Jze'E

, z ,-2si1 Ûs B1@

a1.ile{Krf 6,p"r-Jls-if

'*1'ut

www.mat

hsac

adem

y.net

udlir.

grLalr

99L.an

ù9ut

,e=3+i J3

c=t-iJjsb=l.tECe B ,Atat;tl

3-i 3-i r-i ,.t11* o^*'stz:v'!to

2 _- -. _- - yI;,,,^, (l+ilz _3+i _0:L,rrl+i l+i l-i ' '

" =4Ti =z-2i.éwus

1i 1*o aao*".1r ap.lrr O

Gtro.rs:..r) g 02010 - 220r0xe505io ,*s z o=2i - 2eit ,t;,-tt

7 r2or0 - -tzolo :glltlr3 erwsilr- sifr - -1161 çlâe

.r-.lL sQÂ- oar z92o1o rg3l

. ( t) irÂ lr,i' tl a1f-. yf I

-/ l; 6- \ -:3tr-t + i - Jzl -1f* #i l= {2s' l,û.t I t -; I -.,Æ,r+.r\r")r'

21 z"iT 2 iÆ+4\ :'î*t4*Yr @

_!- = :-:rr --+ e- r t * i ) ^.

-r r r_ Jl "-il, " r= 2 eiT,qrtz 2 Jie-,ï .,lZ

zt =,f2eiW,Js,

zla

www.mat

hsac

adem

y.net

' vl :-*..*4 .-*l 6

,É ùir gr& g r:,Ji, M o(zo) oÉ* .g.ir ùr-rrJ.t :.5. ll e,.6,Jt 2; n, i-:' -:ù - e' | : _J,,

J :so M'(z) r}us 7a (r) ru;E

z' = ê'', =( * * *t lr,*o ùbrrr |Jô, ;:<,u qu(,r ù!à 4J,e\z , /gÀ ûf.rsJl tia2 z - -l + i.6 ,-"' ,jt:r M âJ.iÈ)t ô,s.a !!s *f

brb.e

*1g z ' aÂ-wl ûli M ' u.ill

"' =(* * |, )" =(+. +; )-r * ;f) - -.6 + ;

( i) sÂ À-,*,^| 4t"yt G)

AC =lt, -znl-la -2iJal -4eAB -lz, -zul-l-al =2,r+*,

nc _l'" -z"l_l_ztJil=zJi ,AB2 + BC2 = AC2 ,t+.,J.,tp| a{â .,.g

.B ttal é çlu lBC,. ttu ù!À rleàli.ô i,.!- s"ic .*ee

*: ,(o;i,v1rr"irsu ,ur-'u fl*$ |.Jj vs,*lr 6r:-u é

. zn =3i s z1- 1 + i :11p;rtt,ete tl4a:Â,\l qlSl B 9 A

. Zn s Zt :6,!l Js,âJt d, \.ft (lM' ilL.'tt Z aÂ'.t)t tB M etoi3rt! osr g9.iI /Lf, qLiJl

^t ûSJ (2

z'=2iz + 6 +3i.Lo z' a,t\sl ols

. ,S ,iq$ atârll ô.r,*U ,,,ct rJl gic -i

. S;r.ll a,t tst, A â},ilt 6,e- C îbill tJ,\ zc &e _v

www.mat

hsac

adem

y.net

{U : z), (n ; - z), (c ; z) \ ataat a.at s,_ r. D n--.r 6st

-DaLÀ;rebyzD ;iÈ-l

. ABCD ç\-flr.::L r$lt el iir -n

(Â) Osls z ta:a-s D ,*s B V r-Âl:;o u$*U ûâ eËÉ MJStj (4

1ss 2-- - kf.j ,i" ù* srI Z âô'y)l c,li M ,hnd Ar9,o,.Zo - z

.{t),lt a- z"- 6 + 3i;;-v;r ûts E,aÀnr,t ;i g; J

. (l) a"rqff iqp,i- .zr - z -,sJ;ts.rrJt ô.r"osl ro ..r:.o rr"r-.* g3,i -r-,

Zo - Z

z,q=l+i:t4JJ rs.,lrl ,,1S.ilt éezAao.t6 (r

1+i -.1t

zn-lai-J1 etv,;5!;L

z B - 3i - 3 é 2,o,itl,.1s;.tl Jc zB 4ts Cs

!6.iJl ù'ô ^S ùr'.r! ,r(ru ôltt.*Jt gg Su]/tp z' - 2iz + 6 + 3i t;t-ts

S3ie',";f af = 2t\U.s b-6+3i e a-2iV, z'=az+ boi.r"g 0 = arg ( a) - $ +st:, k -lal - 2

^. 0... -Êq- qur eÀ

bz a= :-:d lé aâ1*U z9 An'yrt {rl5 C) ôr.t âJl ahÀJl-- l-a'

. B a!.ir eô str. ,l ,s;1 zn-.b ' -9*1'.r!-* ?i- =3i:u.,sl-a 1-2i l+2i,,S ;t, U t

'.1âtJl' A âJâtt)l ;rrn C el";;Jt âiE t zc Wer -r,

:cit

^11 .us

.'#)

www.mat

hsac

adem

y.net

zr=2izr+6+3i -1+5i=us z'=2iz+ 6 +3i,r:,.r1

.ABC,' trll àeJ 6r'- -1 --n

e=:-, . f, cr3[ e 2 t, .1 6i!rr .tJôrt U +W)\ A ô,f 9Â C :qJ

.fi zr^;!1é ç,U lAC.. r*1 gi

,D zhl;Jl z,t>\ zD err i1l

Jp,Jat .s { (A. 2), (n ; - z), (C ; Z) } et";u arnal s>. y .,,o D,u,.rr

1- 1- , a-- _.aA-z'--. -zo--3#2 -5+3i \:h6 âÀ)sZn

:ABCD .,c\)l i-:rL ùH*i -.,

ZÈ =', - z,q =-1+2i -. Ê gb,àJl ànu\r : b-rr

Zù -zc-Zo--1a2iaDT eb;ll i.Àz\re

(r)... e\;l ç:tszABCD4IrI ,;g;ur,.ed- El ,o^,

121 .'8C * BA 61 BC -2BA Al g:ù ( v - z) Jtsàt us

1:; ... ,B aei:.tt é (6 ABC ''.t.ll ;Î u.r-.e (+ -2) Jt.-t t>.s

. J.Ltu ABCD *\lt i)l ër,:-r (3) s (z) g (r) .r

'(Â.) g1 n rszr-6+3i aa-ylùtsEaLëJt gi,ge"lr _î 1+

r,.-.s.girr- ,u ?t - zE .t*, zt - zz - 3i-6-3i

zo-zr zo-zz 5+3i-6-3i

.(l) U ç"- U iLn:l ùi è.Ë-i ,t.G

t oB - o frtl l.rrll ôJ.rJ é,r:gJl .;1..irtl -\J

Zo - z

u's(L-'\ '\'" -) )=\

------>MD ----'MB )+2nk , keZ

,(l) a"r.nu ùH"r r.--

www.mat

hsac

adem

y.net

l.l5 gqgr eij> rÈzo-z

keZas(d;

.[aof+r,,uJ'r" (Br) e.Âk$ ** (Â) a"e"+rr ùp Ctrlr

t (l) .'tt ùl.a:;; !r D e -B ùubÂr,r ) (a) = (m) - [ro],i,;t

.2" -62 * l0 = 0:ilsl*lt C a,srfr rtrrlt àrJ.+. élJ|, (l

B e A s';h;;st s'i, (O ;i, vl,,,iltE:Ue rcrrû C!$ d! yej:tt r5sa.tl O (z

.Za=3 + i, zn-3 - i roorr;,'y ù.ttt

.f +stF A o$ 6JJl i1l.le.rJl r ,i{te

' z' =iz + 2 - 4j :*a r i1l.pr! arsrtr alwl 3ï 4 -

. r ùbrrj! $s. D g z c =7 - 3i rçt-l é:Jt thûJt C (3

- zp -5 aJi zç D eLilt a;-rt 6i,9i* -

MB) - znr, çi atg(ffi)= o - 2n k :us

B

o x

www.mat

hsac

adem

y.net

-W,as ultFr rË ffi = ;r.:i é É

sc,ljf

,z2 - 6 z + l0 = 0 arulrJb r r

,foo ù41;. ù5.r.,Ilr.!ri ôrtCt 3p Â < 0,1rS rS1 :nîtS

- --b+i.Æ.---b-iJ-Loz-----T- t -r-----1î-

L = -4 - 4;2 - (2i)2,9i1,:t*g ojo ii" O

.ZZ=3 + i s Zt =3 - i:tco qfr$" .IéJ" ,1,!' J.r, ôrLetl O

, z'=iz +2- 4i sor g\eJ! aisrtt ôl;(l ùt ùç (2

,JQ os.rr çirre0 sÛt Mo(zo)oÉr.,e,iJl !l.le.rl, qs:tl a|sfl \éfiz' -2,, -e'a (2 - zu) ,u M'(z) nâ,t1 14(7) 4^73

;L ;4e" 2 -i s z,a=3 - i 61 çt ;e z' - z1-e'1 (z - ze) :i1[i a.lce

.z' -iz + 2 - 4i ine z' -3 + i-i(z 4 + i) ,uoû .è_g*:rb.e

z Zp --J +3i ,e D al;;t aa-v;l éôaJt (3

z o= i z c + 2 - 4i - i(7 - 3i) + 2 - 4i = 5 + 3 i za,as r (C) - p .r-u

't'ZD-zB -zc'zn

5 +3i -3-i7 -3i -3-i

,zo -t, _ll ,iigror"1.izc-zn z

2+2i 4+4i 8+8i+81-8 r-

-=-:.:-:4-4i 4+4i 32 2

, BCD ëtrlt i,.0," 6tr;-l C

---i t,.\ n -t1 .t 1Afgl zl l=i ql:r l=a:Lir.rJ"\2 t z-12'l 2 '

*(?=)=îulffil=j,gu,,

www.mat

hsac

adem

y.net

qÈ' È) = jBxf ;*-zno -;; "'o,_

3 zt"t:tt é ëg BCD e&r.f gro-t

, ZB =J +4 i zn= I'bn-lsJ 6;st D e C . B, A t;;tt

z o = -2Ji + i( z * Ji) s z, =2.fi * i( t - Jt))qt3i *l,t:s A of* ç.:)1,;l.)9rrU B a.rs- ,,o D,ii 3.;1 _i 1r

ûu'i ,:.rLre 1,";çr^ (f) ajtl ,rb ,3rrn: D e B q:hiril gl Ger:-r -c,

. |ôJLA r ; -i

.!,',;s B ofc6ll çlta:rL I as.,o F 5S:s 1z2

.-2i q F a'aa], zp aa;t 6l;1;, -l

.[co] a"r.', . â.-":- (+.F ;la:rr ;f 6 -e,

.z=c - 1j s.sts,s,lrr ;s;lr éu,-trzc - zr _-iJj:ûl c.otl -.,oA _ êF

lCOlr*.,tt aÂeilt )yâ e^(Af) gt''.*[r g1 arurr alr-irr s. e:ar -

. D eC ù,tLÂ:I 6;:1 , F e B,A !.irl st tstô:et (3

: clJla*,+ qsle l or5,.. .9.rI ùberrL B ôrs.a ,rr D 3i 6ç i 1r

É osr,5i.lle g L-s 6e M o( z o) ofe6JJt ll.prll ais'1t ôrq*l a -j fz' z u = sttt (2 - z o),a M'(z) -^t"ut U(z) au,l:

z' - zn= "'T

(, - zt)re ùtreJt l.j+, a:Sjt qtdfi ,3p ,.r-,

, -+--àF , \O;u, v ).*tsr"e uka etg rJ! V:*fl Érft se:-ft é

www.mat

hsac

adem

y.net

z st - zr= et= (z B - za) -jp ass r+- B a* É,zs E

". =

"? 1"

" - z1) + zo =(- +-, +)(t + 4i - r) + t,o-,

:-zJi+i(-z+Ji) \ /

!.6:s Ao;S.;c ,9,i.[,irre.rtu B a.rr çD $ çl zr, - zp :i't!

,l'^,;çr^ (l) ajts ,)c 5reis D e B q:ea:ff gi 6tr::."t -,-r

en - AD $T&$js Ao;S.;c,9jJt ùl.rgurrr B a.,e,,

"o D 3i tr

AB -1", - znl-lz + +i - rl-lz + +il= ̂ [* +4 = ]/j :erre

f :tî't1rsi7ro 4 (l) arlur ou or*il D r B oru;rr .ii cs:-o

.2"/j r^,rr-a . :";,

, -21 oa F zLa:t zF aâ'yJt Oi Oç i tz

.1(16!;1 s.rJrek.,,, r, Ms(zs)ogy6ilfr*dlas]t ôrLxrl ,ÂË

z' -z n - ft (7 - z u),f u'(z) at";':t M (,) tr ?'

Z' - z r= * (t - t ù .e 6l'Ét,l lr{, ;.(J !l ;'tbS.,l ùlr qles

? ' ,l(t-r -4i\+3+4i-Ji,uszr=â\ze-zB)+zB= z..-2i ç F zs.xls zp âÂe'!!l : ur'tt

, [CD] ,-.rtr s.i-::,. ,r.o F ;r^:'rr ;i 6l# -*, i

z c + z o' r"lcDl :-L.rt *iior.,,. Àô,y i

z-, lzo _zJi+i(-z-Ji) _zJi +i(-z+Jj) _ __2i zt;.;$g22'[Co] t"^tt r.i,o:r,,.o F aht, , ;;;

zT!-=-iJ3 Oiciu! ".-

www.mat

hsac

adem

y.net

l+2izc-zF

=zt-Zr,'-c '-F-t,t J!o9t,1(.Ulgbr:..1 O

";' =";' -

Ji e-'ï ' i'"!.utgf iJt)= -i 'l-,Æl=J5'rrur,[CO] a"oa-fr i-t^ztt te?6 *(nf') p.a-fr ;i gtâr."1 O

(- \ ---+ -->oF guqs argl ': l- ( FA : FC ) - -+ [z r] ;l or,r

\"n-tr).sr""r.- (,4-lc')s (cr') o*;J

$DsC, FLâ.tre lcolt-r^,t,::ir e-o F ac.ôr,l ùT ré.s

.,ir*t*" (Zf)s(CA) a^ra-rr Op

. [CD] a.rr, .tr irL:rl ;sre.c s" (zf ) g.r-rr 3i er:;;:De C,çÀAlt

"Ui1 1:

.B âhtuJt.'râ,Aebil r\j!^ e$ (l) ôjhl ç-i*s:s Aat"xll;$ Atafr,,lr (t) a;r*l ,lo ùt ii Cs D Jr*a;st

- AC - AD;ur,.e [Co] i-,r' t I e'bilt )t*c èl

.-2i a;-ytt ots F ait pLi

3l te.e. F au.lu;,9i1, (4e) g;"-+t str 6àe.il(^h+:-{l Ê-,. (A)

"r" ùt*i; D g C ,$hiit 6l ,6';'-:[CO] a"rnt :* ss (AF)

. (A) era-rr, (f) a;r"l êbui uhii bs Dg Couç.rrr

( e.rul ÂlétÀ,| c,'3 AÀÀr,l * D s a.'. ell ala[ôrt cJtS ahÂ,1 e C )

2Jî'"€'t=-2i1+2i I-2i

www.mat

hsac

adem

y.net

G'i';t.w:''p"

,,ti , @;l,i).,..rt?,41e r'rt4l S!'ll rjl çs.*lr f;tl 6er."[l I.r+pl U' Ji + li r J3 - j rn.or'i-v ,gu B e ,4 ;1u:tl

ùr É B él A ,)':"lJ O ofr 6r'rl ^S qtal, aiil ôJt'Jl Y5l (r

,^-l-\t 6;oJli

,JS 'bJ Ug At= A:d t0.5l.51t1 'gJÉ-ll

!r. !âJt iCtt ' iJ-t (2

. zn $)u An âÀ,! Jl yi . An*r = S (A"), n g* rs- A2 e A1,As ûârl \4ll .5*-$ é C;ci -l

,fun n\,, -2(Jt) e'\-T-6r "l J,.t -u

(OAr) S1An"^"r br.J o" s"ti çln'l*.ttl slrtlt a'e'a+' ùit --'

:,!té t\>-tr(un) aolt,,rr p, t:.n ç* s.r".l5 J-j ç Un=ArAn*l s Us=AsA1

.q4Â-1us,Jsll toL &rt r.rh a1^r,r a/a (zr)Of 6 J\

www.mat

hsac

adem

y.net

.rffqtï-CÊÊ.|Sn=Uo+Ut *-..*ltnt\z Sn &|"+fl. rt At{. \.,--l

lim..S2,.-.-ul Pn-)+-æ

: cJJl

r ,S qLa.r! ,ttru ôrLrl AtlS (1

,.z =az+àJtàJl ù.sriLll qtàll ô;Ç

: t7 ., -n7â[ r S(O)-OI a_t{r ;a;n, l.o-"-u, ]:iÉluJt.e .l :).-.( _,r+.rtla=o - lzr-q7t*6- ts(,4)-B

z' - J1 iz ,r"o S a.,LLrll Àértl ôlLrll :i5!

0=f12.æ)lo':t:sk _ Ja +'*-', O of,",,S;r,u arLiJl ,.aus*

:gllll çÀ;*:ll Jl.s:.,b iôtJl â+ÊrJl |.'J}"-ôJ {Jt ,l9,.eJl ùt g

0 --rr;s (É > 0) k +-} , M o(zù oir" .eiJr /t+l qtàdJ :r(il ôrLt':tl

z'-zo-\çsis(z -zç),uoM'(z)au':t u(z).l,, æ orr çlr5:,|

z' = iJi z = J3 e'a z',*J'ee" dt'l1e

JSIJI rhil ,A29A1,AoLa:l '1,àj! i(2

z3i é!;;; Anal =S(ln ) æY*rr O"

/- r riâer(Ji;ù û5!.zr J3 e'2 zo=J1 *3i,a:ns A1-s('no )

4( ilj ; l),ts1 . z, - ^!! "iï z r = 4Ji + 3i,a;.s A2= s (,4r )

' "n -2çB)n "ilry-H sisuar-e

:;i e.r:-j An+t-S(A) &!rrl o.

www.mat

hsac

adem

y.net

zrJiëizo

z2={3e4 zr-.8"4rÊ"4 ro-(l-tf "4 ro

4="r3e4 z2=.Ji"4r(.lif "t+ "r=(Jiy

}+ ,,

"n - Ji "tT "n-, =(Jù" ;ry zs:èt e,,rr,à

zo=.,fi - I -2 g-iï ,;)1rrr-t aiet *"iuz - "i(9t0r)

,4,.or;..r1 ,pe

,, = 6 "'l r, -, = ({r)" "'

T, o = (E)"

"' T x 2 e-iT, tt é,-;

,, =($)" à T ^z "-'E = 2(Jt)'

"i(ry-#) 0,,

:A.rl,| e+iuJl flrtr.,b. ,4rS9 ,lr-1 eÀ.Ê Jt .ri-,| ùS{ :2 ,.q)b

, O abju'fi o:5r. Frr. çUiS;tf n1 a:I é*;c,hlâ:r, .:fr-,Â|,-rù.

tJf l ,J*Âi al ;t . arUA; 9o ,S dl&r)l ôr. n \7r^ ù!i 0 d;rJtj9 k dq.j

, , ,, Jnn n\ ' no aePtis kn "t 'i ' Q

z, =2lJl)" e' tz-r-'/ g; ùr.o.ilr eEb4 ùtÈy'r Jr.--..., ée ,s aq;b

tn â,-..Ltl rl.rcll irgrp ;ge; _.9,

y - Æ x * (Oe, ) e.-r' arh. ù!ô Swr.ls z 1= Jl + 3i ra A r a;,,y

targ(zr)=E+ /rrr I crq 1A,e(o,nr) 1

. Ëe IN e.,- n -2k +| ztl e;u; ff - f = ! + t n."^s.trrr3 Lr^ô r,r.r.c n 6S q(O.ar)#l Jl A n il"â;)l s.,::r .ùsl

,:o .iro aol:r. (a, ) ,ii oç1 -i 1s

4gi.r' s.r" rr.e rll l^:eg lst+ûô Ca(ur)l;jj

www.mat

hsac

adem

y.net

un+t=4X F.Fel.t

- t t - -4 n +t: A n + | A n+2,c.9-?Ç:t' r.d*1 f;1.r1

(A, , An*r) -1Àan 4jlrfl ô.rr ùF S J"àçU qLul a;o.S a-u.ll 9..-An*1Ao*2=

^!î Ar7Ar7*1*$.(An*, , Ar*r) aobat*rtJ *or.tnaç J3 iln:{t;l\e

q -Ji Vubuo:AsAr=4 sryt rôL 41-J,rÀ e4'o. (rzr),osl

Itn=\roxQn =4(Jt)' :rt 9ttnrô.1rpgu::at -i-,

: S" es+lt l;l*z -7

's n= tto *, t * ... * u, =,, x! rl" )t = -z(* /t) [1 -(.F),.1t-qliT, {-, =+"":Jh,rrg lim (J5f*' =+.":ù1fùri ,lim

^sn vr...-n-)+oô n__>+l ' ' ,r_++oo

A3o

v

2

1

.Az

-t -+ .a .2 .'1 O-1'

12xtAr

llne"ti"t r"i" zoos sn t

z2 - 4.8 z +16 - 0:ir.:l*[l . C r.(]!t ô|rrlt àre.+. é ..J- (l

www.mat

hsac

adem

y.net

. (o ; ai)-r"{b r.ldt ér{| sq ln-rlt !5lt,t,F-tl é (2

4:28 -E.tt:26 +2i --..iFt urr bË"te, r,il C t B .Aùiirl j=i.zr-4;iï ,

. Ér!+tl JS,àJI 4t Zç V$l r.rrJl l.51 -i

. Z c g Z n , ze ;y éJ Êræ5 ilr3htl ,;[c -u

ë3É \.fl'- 1 O tsf* srl ôrslJl rJ! rrs:; C e B, A Au ;f e:;:-t -q

. ( tôJLô ùr4j

.C s B ,l Aau ç,to -r

. çut ,get-:c IBC eÂtlt;1î c..pl -a

.B él A Jye 6,tJle O o2Se É,iJl R ùbeJl r':d (3

.R gl.;g'rtt 0 4ebtt E:pt4le , zB

= e-iT ,Ji ,9 n -izA

. OAB ,,.t.lt irllr- g*lt -9,

. R obgu.lg B ;À;lt r.r oa C al"z:t ol,* --a

'OABC ç\lt aeo'b er::''l -'r

:J)l, z2 - 4^!! z +16 = 0 irs1-tl rJ- (r

Â --16 - l6 i 2 - (4i)2,9 ilsbll oi.o.;1.o O

zz=2Jl -2i 5 zt-2-$+zi,t4^ùFtj"ù/-igraJ4t O

:6aa1l j(iJl ée z C A'.16 -l Q

-;fr | t *\ I-'i - +("o*(- i)+ isin(-i))= -ot; Zç s Zs , Z,E tr ,JSJ ôrâe9 abÀrl ùgri -e

www.mat

hsac

adem

y.net

1tS=,[@E - 4'û..' zt:28 + 2i

z,t:2Æ+rt : O(+-

*s("r)--utg/\

arg\2.)- f s

*eG)=[ slzal-a,:;:

zs= 2^!1 -2; =-Ç srO( E)= - Lu' l,,l --l znl- 4,o,,s

zrl- 4'o,,e z, = 4s2 iT .6-116

, O r,o5ro .,rl ôit{rl Jl s^;r C e B, A u;:t li ë;::-l --7

oA = OB - oC - 4,obsl zAl=l z ul -lz rl - 4,ras

ti ^rs O r,rj(rr lrrll ôilJl J! *"r:; C s B , A loll ,3i g:::-l

, { | â'-jLâ

.JS.àJI rEûl , C 9 B ,l S.;.tl e,Ll s

:,1iul Égt-.rr ABC èt,ll,3i oti! ---o

a c -lz c - r rl -l 2J1 .+

2i l- 4, at -l zn - z

"l -l+il - 4't;'-.s

.B é ù-,iul ,e6t-z ABC éJrlt :,.15! .fi1- SÇ:ue

Zp 4 e-' 6 -i! -i+ -i+ zR -i+ .: = ---------=- = e . xe ' 6 =e 3 : 1!- -€ i gi.,gÂ*lt -l r-r

zA 4 e'È zA

, R 3l1e.rl 0 a19rYr 6rr-l O

:,.lLe jJ 44.!i ô.,1t+"JQ :5s

é opr g.jJrs 0 qsljs MoQù o;51e ,g,iJl irl.;e.trl ':{r!l ô1!rll

z' -z o : eit) (, - 2,,) ,ç M'(z) z:"ttt u (z)

www.mat

hsac

adem

y.net

z 1 - zo -- su? x(z,r- z ol -.! 7 " -

fl rt "*

fu- = e'l 1artzA

.0 = -â <s.'J.]E O of*,g,iJt .il4,.rn ,1!l ôjee *o I ,ii {,.r1 l.bg

,OAB è:'11&rb grr'. -1 ---

:18

e-'1 xz" = e

:ù6 lsl L;À5 l5l e)Là!il s",-lazn ABC ,'-rtlt irS'-zt2li

- :11zB _LB -Lo =€ '5 ,lu.slzA Z,q - Zo

f4'#,)=+ual;,(ffi)=-+r

on - oA.*s ffi = t,dlfl= I :ù1 è.:;:-:

çù ; 6 = - !lzn!,et,,s( =)=

- !ïzn),s,\ze-zo ) '.zyÀyt o"$b oAB ôr4r, ù51

, R gl.19.rlt,,B ahi:f l\ya orC Zht;l; irl Oçp --:

z' -- e-'i xz,*o R,i59.rtt af,lt ôrt.*Jt

,lt" o)-t4 -i4 -'17* 6 | -;4-3x4e'6 _4e \- - )_4e'2 =Zc,t:,_,t)

.R ,itrrltr B aJ"al a;.g,o,ro C aÀill 3i O.= li.o9

zOÀBC sc\ll Àr*b gb.:rl .:

Za - zc - 2Ji + 2i.g ze - zo - 2.1-3 + 2i ,ru-,ts

----+ -'>

.OA = CB :ùl s,.r: liÂ9 Z,l - ZO = ZB - ZC ttùg

www.mat

hsac

adem

y.net

aÉ6y(HE glbJût( ,JE&flc. {ir ùt-rtË" ùtr1b" ol'1,à ) BA _ BC âS Jr ôôltj

.(o;i,i) ,aqrue sh:!r e{Etr j! ur. e.",r ,. (:!r ,ss;-ll

. z" + 42 + 8 = 0 als|.ctt . C;içit ct.rrlrt ir.eg.cc.r ,â.,.t- tr

.eil:fl r'Jt Jl Jr É 1tJr+rt J{àll {jte Jel'.rt s.h"

.b=-AsA-2-2it+.ot:aryé9r-11 û. Jr-L,z B 9Ap.ùJ.rrl é1.:, é JirJt ,Jt Sl g;ti ,). B s A ù:hÂJt û1, -

.fi +tt:t O o:5r.o 6JJt ùbeJL B ahn:il ats,c C ahazst ai,y dr -1

.| a:3l:s A o;5y 6jJt ùtreJL C aÀirrt i,s,- D eo...,i -,_r

d -2- 6i ot D:t-;.rt a-v;i 6, -

;ABCD ocqrl r.4 t" . D 9 C,arhul prr _q

fA,ji4l ala+rl e*Gu *r";. çr.r* 4l èÂi-srtA@

-=- ,.:- rO08 S)

- r'rrlres Etranger" lrrlrr ""I Eac r-*'-'--

---"=--

www.mat

hsac

adem

y.net

t (-,1 ; t), (a ;- r),{c . a) I. ù er'-ravq do g*r s' ; -î

.&t +U àiÀ é,iji . IR' 1t9.+tl d e-e-l'v Ga lÀlll arsrSe è:::ul -9

z D,1' Go Oot";s I A 4,iÊ b -q

:q= gsr*tl ûo M J"a:l z,.so4. û,,t"1, itÊ . a - 2 Ol Ji!-Jl liÀ e O* <t

ll ui-ffi+ 2Mëll- 4Jt

*tl,22 + 4z+ 8 - 0 àJJI*U J- (l

| (22 + 4z + 4)+ 4=0 1 cl5-.l zz + 4z + 8=0 I :l{'rJ

z + 2 - 2i s1 z + 2 - -2i ol e-; Q + 2)2 - - 4 - 4i2 -(zi)z'ue

zr-1-2i -2rli

Zz= 1+ 2i e zr- -2 - 2i ,bo 5tt--U ôsl*ll !b :jil

. Z2s Zy ifliLl ùle.Jl q.'J, ':+tl uL.- ùt{

lztl='t+a -2J1"ctt)

-#-'#)='n(-+-'+)'*,,, -zJ|("o,(-f )* ,'* | f )),.,,,

,r- a -zJ\("o, f + iri.f ),, C abl;J't en y lhd _i (2

.l*.ser çJJle 0 +,-ebe Ms(zs) oft,-,s.i!l !l1e*11 tr(.,!l ôlLrJl ,-éfr

z' -zo -sis (2 - zr),a M'(z) au':t M(z) at'ui,

www.mat

hsac

adem

y.net

z' - iz --vr I -!rs o of* .lutroure-iâlbà op

c - ib - -2 - 2ia1i z. = i z ".t;ne,d -2-6irf D,bâltai-V,3i;,=,* -=

;E ;71

d - a = ët (c - a) ,r-s zo- ze - ëz (zc - zu),qtt

d -2-6i,o;L,ABCD ç\:ue _:

6 - o - (- 2 + 2i)- (z - zi) : -4 + 4i,f È Tuat a>v

c - d = (- z - zi) - (Z - 6i) --4 + 4i,ç,o D?grarr a;-!

. erÀ1 éjtel,^ ABCD o,q7t ,3t!. Al= Dl ,o.,----È ------|

t BA gtc'ÀJl AVq C Ga gbâll .1c {,.R:rl -i (J

, (a ; - t), (c ; a)j ;r;+u ârac.lr et et G o---+CGo -t= pl :a.:a9 AGo -

tIF i"g.aU a g."+ l^J;s Gd JoÂ:Jl âr9.oo.o 61.'....1 -.,;-? -----+ . ------) | -----)

ûtt^t\f 6A e CGdtttvill ùl ê:,r; CGa _; BA $tetÀt oa

f:.o:-.f l eÀ ff irg^"f l d e,"+- l^.t;.c Gs !.&Jl ar9,o+. ù!i llJtr.g ror:,

(CO) s (ZA) çala' ùt kr (lB) È.ir..-! éjreue C aLnr,b rtu

C fr"b (CD) e*:-À | sÀGd hilt;r.e e." gï GËr ùLjte:.

t D SoGo û:Àii éJ A;^â.â .i,

( g)tôl 9:r9r" ABCD .-'t.lt) d -ù ,s\AÈ - O1lau

,dur,.s { (,1 ;t)------' ---)= AGa- BGo

+ ----BGo + aCGa -O

l-+CGa -; BA,ç1tl

D é' é,,!s Ga ôts d -1 J.l.r.,,;:l dâo - j El,,au,- --'--+ --ù +

' ll Ui - uE+ 2 1IZ ll - 4^lt ëp M t^â.r I a'e.,." ùb,û (4

www.mat

hsac

adem

y.net

,.F J"f ù. d*,{ (l ; l), (B ; _ t},{C ;Z) I ut @ g.* ê G

- - -+ .+

AA - MB + 2MC - 0 - I + 2)MG r- 2tr4Çr'4s/t 6a I'l zr^;z

| 2frë, l= +.lz ç;*- lfr -ffi+ zÈl- +.fi ,"-,.).lj. rn,. ;-it Ç, r.rj(rc art ôJjlJl çÊ q9$U lirl &sn3.o :çj.:!

Gzet Et ti iSllrrl Jf+r:-Lt ,G, 't;;1O. [ca] +""r ùdb eô

'aPr.tt "Ui1-Of- I\vf = cG, = /"1) :a:ne CD =ld - cl-14 - 4il- 4Ji ,'et---+'

ll MA - MB + 2MC ll - 4"1 2 qr'f çr..$ v M u;st ioe.ca,o :i;,!l

. C ;,ÀÀtJl.t^..o9 [62]a'r:l ei,a:.o G, r^,jl,^ ,,:Jt ô.r:t.rJt ,,.o

--**I-"'*l''::t'Ï13

. . (A ;i,v-+) d4,brue &l^*r[r Cr*.U st! y.-^r. : <.r !l \9ei.*l'

www.mat

hsac

adem

y.net

t' , fÉC;,fÈr.r-l

' a -\ A raf*4 (f) aralrr zt = 2 + i a;-';çcrs ,4 4ar 4u

zn-zu

Jl "...u

M âh;r'Jt gi ,ë;,;-"t . Zo-Zu t4tt ù&! ôJ.c,zn-za

.ôop. c{|'. yt s1.., g atfé! e+ ,]i oto :|s.r p-;t 1r

- (o ;l) ,*tr s(f)er* Àô é,.rt.i, J (2

. zç - 3 e z6 - I bôbi-\r ùil,l ù"u:l C e B g*t _,_r

. (f) ryru .Jo lrrÀl I :r^r,'t rê . D ÂLn.1Jt eÂ",\ z D &È -

.1 *9i ei')r,t itt! âL^,tt M6t e5 5-

.ro_r, éUt c.rrfl ç,....*t _i

l*,.t .o yl3 -1.'

. (f) ir:rr.lôjlJ-l Â.iLj ëL.q (AU) *-,-u .fu.A1*ar iits ô,:trrr (f,)J r,j (4

.lr.e;; 6(I").orlr*. (lnf)s (OU) v,-a,'"dr oi c.;i _i

.NacÂl e),cF -v. _ | a+t:s B of* 6i,t ùbeJb M eÀâ,t i,go M, oo; 1s

. .1s4, is;.Jl ai,'V 69 _i

.(fl) i;ru é!u*sM'au:sr 6îc*ri-e

sdJl

. ,JSrJt .r!i:l :ç-:ll (r

, (O ;ï) r*tr s(f)es* .trij o.ter ûÉ3i -i (2

www.mat

hsac

adem

y.net

t -ol? ( o i ) :r.r-- . (, - zY +{y -t)Ë - 2 {r) i,*.r a*.

x -3 i x -l éc ,:-a 1 E -zY +{g -tf -z at -tr ,1-'3L v-0

3e l u.ouov 4*.i; g (f) a;r"lr ,J",tro t*êh4:ù!l,,9.1;i oQrb

xe k,!.- z - x e M 'rt-v .(O ;i) tot, ç zt-at llf 6i!

l t - tnl- Ji .us AM - J7 ,gts rs1 (f ) ôa ','^" M ùes3

x -3sl.r -l,ù3! . J(x- 2)2+(- l)2 = 2,..gut.e

. D abnll a,Âr\! z D ;tr"i -,)

AuàÂJ ûp,jut.e, (f) a;rsr slr qrhÂ B ahirr ô*û 1ÉÀ D aLirl

. fn o] +,lnt r-i,a:rr,,a

7,!Z_zo =2zn -ZB =3 + 2i ,o;n9 zn =7!12:\t)t +zi -1-9ran-Ll, \ \ ^- Zt't-Zrr

t-t,9-' \J. { fr.ZB-ZM l-+-Ët za-ZuJJ

7^ -;,. ,+ +\ Z^-2,,arg ry - | MB ; MD ),4 ôJâ', é."{:,e,1 r-.i:rl -.i- za-Zu za-zu

." r'U ùF dlJL.s ( ) - aryei)=l [zn] q..r ,su,-,vr

[fp] "rr*

(,:'ll ôrir.r,r él u8 M zt-e'q 61,g'u. M 6 psu MBD

(r),.J1 e":rr nf ahôl û!i (f) ôrlJr ,rte qr.! B ô+!ù no D oi tc.s

,it\:ts-(AN) s(OU )a.+'*tt ol ots!-i (+

.6rr"r.." (mr)r (,or

+MB;

+MD

,lqr:-fr gî e':r-;.N 6 çsu IAN èl$ ùF CUlp (I") 6. ;t-:, fy' 6i

,it."l-r" (frv)r (Zlf ) ,*,4-rl ù!À (Bl/) fiLtl ùô ;Lât N ùl

www.mat

hsac

adem

y.net

,s MBD ean I ;J1,,*.. (DM) r (trltrlal+ar æ A.(eN) s (OU)iÉ.+-u rr.,F * 9ry(Blt)çs-rrU,9

.tr,:rç- (eu) s (oa) u.4-l,; :i

,N ahill aid;!f -.1

,[AU]"'t 't ù.;L:r if . [nO]+rr't,.;-,,^ os A:BDM e*$ 6

.[nU] ".:"U. ;.'. ^ .Ày' aU:ll,;1 er::; .ûu)trb (AN) s (DM)

- -za*za -4 , 3: ...r,r----1-- 5-r5r:q..3, l1[' zt-a'\ ai-\, ùg"j i (s

- f; +st:s B of* ç9il1 ll:r,.rJtt M alaÂ;l ô,g- tê M' -d.rrl

,rl =t + li'a;i . zu, - Za - ;iT e, - z6 ) :,!at1e

,= , (t") ;;rrrr J! t# M' aua:l 3T or.i1 -9

$ r" (f') ôrjfJr rhs u-i,;1 clu .48 =lzs - z,tl= Ji,v,-tt

;, = z+

-- ] * |i ws ilelnal a*ai. :. .'^ 1 ùj6 rsr

_ rM' -lzu, -',]1rt - ftil- $,ru,,..,,-'t;(f') ,sl f trrË ù,âje 1AÀn:I rrjf.ro d,t ô1it,rl lt .rcri M':.lS!

www.mat

hsac

adem

y.net, ++\

.\O;U ,V ),r",t+r" r r.trr. er'. il! u. Jd. rtgr,-U

:\.iirl dr 1v.'pllet çltce B', AJettt çs: Q

. c -ll + 4i s b =5 -3i, a- 2Ji e" a

ç{+tf JS.àJI Js, a ' I TrLl s.rrJl ,:-dl J

.Ce B,A,h.aJ eit -,-,.

.,1pl*ll ,get ';.. ABC e*tt 6',i 4 tz

. z vltll rrE l t{,.Â'y 6J;*tl ù. ô.À5 zr'zz l1t[ ,91 1t

'lz -b lslz - al o" Js g'r'erl r""irl gei -i

.lz - al-lz -ô le.r..9s'*tt ,5" M t";;st ire"ç" (A) g.,rts ,p -v

.d -6+i a.i'Yll ùls zlê;u;; D v.-3 --"

I (^) atr"..f' 4 ùqa:rr D g C ùuhir,l ,Ja -

. ë'ô ABD g'"u ù1 dt (4

.lr.1t" ADBHseqrl ùÉ e.p.l 11 ehnrrl f*t (s

. H uohJl o,:,P à aa:u ç -

r<lJl

:i5.19.tf iJ(âJl "]saX$l s.rrll ô15 -l 1r

.Js-iJf J,tûl :c e B, A J";:st p*s --zçu)t,ls]-',. ABD f,.riu ùT ùçf (2

www.mat

hsac

adem

y.net

cA -la - cl=l - s - zt | -- ffi1Æ +.,

ca -lb - cl-l- s - t tl-.tffi - 55.49t-tr 6er. .^ ABD èliU :,js! . CA=CB zug

.lz_blslz_alu,ff;i,,;

BM iÀt-'.Lt *lz -ol c

' (l) a"g^+U 3g"t -=

AM = BM ês-lz - al_lz -blfun)aât*1t:-Lxtl.re'r. eô (l) #"-.t1 ,o-,

.iJlS.iJl J.Eil , (l) 9,-, Cl(^)ate +tl g1 ,it.oru D e C 6ulalt Jo ---

C e (A) .;p,1wt.e CA = CB ù1 rj"b. e (2) er Jls-Jr u,. O

DA =la - d l-l- a + il = û6 + I = J17,q*r O

DB -lb-dl=l-r-+;l- û +16 -û7,rarsae (a) op ,lttsue DA- DB,a;ne

çsu ABD.*.rqU gi 6r.,.1 1a

DA-DB-^lfr,r--t

AB -lb - al-lz - si1= "19 * 25 = 1ffi ,e.,re

DAz +DBz -A82,..^s. D g

çsu ABD,' r.!t ù!s û,rotiÉ :'^+^ rr...-s

7l{ zt^;'n fu 6,.y11 æ 15

DB - AH Jgr*.y ADBH oettrt û6 rs!

www.mat

hsac

adem

y.net

I

L: b - d + a =l- 2i,,ga5 b - d - h - a +j Zù - z îi*.th:l-2i,i5.

zt1- z ,,.9t jfu!) te;.- é P(z) &P(z)-4za - 723 +llzz +loz-12

:\$ , z {e sr" .J5 .J-J ç .l2ao. B 9 6ç 'a!!e,tt ù,,-sr*rl ,lF J (r

P(z)-(zz -22 +4\422 + az + B).P(z)-O:aàqt .C.a{il rl.reltl ice*so é..,J- -v

, ++.,(O;i,v )r-t+.ttg rôtE^tl f'L*ll J! rrc,*.$ 55it ,5eall I (z

,:rfy'l Jc tsi-le, çll D eC, B, A :!âJl.v=i

.d-jsc-3= g c -t- iJt, b -l + iJi, a=-l.b s a;É*l g4sr*ll gr i$ ô.r.c9 ;t,rLtl iO: -i

.D tC ,B,A,h;;lt fle -e

www.mat

hsac

adem

y.net

-,-L" o ur l.jsr(r) a,r" u' gÇxl rar ;f ;1, +--à,

.(O:n .n ) fhlt -ô É ôrtJl èiÊ f-J h:ra ' :-.:

(f) a;r.l .,tc al.a 4rur F e E 6:ril f s e;P:st ;p -s

.gist ëc A g B é;t:ÊE ABFe ABE ùEuti 'ie(a

e.'"J

F=-3ga-l '\O

Zz =-1, zz =l- iJl' zr -t +iJî -v

. arg(b) = { s I bl-z .ars(a)-n elal-1 ,i q2

.JlS'iJl .1.Eûl 'ç-r1l -v

DA-DB-oc-1 .A îLÂrl i'lÈ3,,a E Àb.a:Jt -.:

D at";:st J! cJtle -],*,

B ahÀJt ô*ù,,o p aÀ;lr O

f =+ - i.l-3 .t-s D afi,,lt d! e..^.rLl

-(o;i,i),F@e rol'r $c'c J! vs""' Éer'4r

.22+22+2-0asuuCag;t slrr!il ar9o+" é.i- (r

:\tp;lf urb bôuir\t ùrjl C e A istÀt Jl.:lru 69bfl é .r*t tz

," =( * -+).f+ **);, ze=-t+ i-L t2 2)\2 2)'^

1L- -; t'4

f*o. r ory "et* It'it'oo* srr)

www.mat

hsac

adem

y.net

-Zl tél| r.&O ôr.Êt il,Jàt dD -i

ZC \.srtl )rrn elrJ,b iie -y

.Z-zc rr,ai G,7-?

:E t :ll.Z =à'1 'al6,ot 7 -

r -'vJ ,31 6, -l2

--T--trO ofr,sJJl i1l.leuJb I ô1e,e gÊ C ûÎ èrrr.,1 -.r

.C abÂtf érjl eJ ,'4 aÀi:rt ole -,efr..i gjJl sle,..jltLt O ô)9,ê B ôSJ (4

.,a,"OCAB çurtr gî q1, B aU:l 6.aiT -

tJ)l,22+22+2=0ôrl*Urje(r

A, = -4 - 4 i2 - (Zi)2,*ast*5 oia ;eo O

Zz= -l - i s Zt= -l * i rl;otbl ùngh, ùl- .JS arl*ll O

r.sÉ| aqrb

l(22 + 2z +1)+ t= O I t;$. lzz + 2z + 2- 0'1 :r,,-$

z + | --i si z + | - i':t1 é;;zt (z + l)2 --1 - i2,t*s

Zz= -l - i 9 Zr= -l + i .tôÀ ôrL{t i,rku }t* :ùil

: Z1'r 1s,lcl.s,*! ôJ.r9 Àlf9.hJl ;Xô -i (2

CA

a 12 - ^ll,ue zd = -l * i z\tt

)=OG"'*+i sin$)-.e) ' + +t

It=.I

NZ2

l"n

(-

arg(zn)-ff 'lzl-..ll,6t

www.mat

hsac

adem

y.net

=zcél);*3*ees

z --'-:Jt 'Û1ùt-'P

-i (3

(Jl _r)*(J: *r),z_zc _\2 2)'\2 '2ï*-t-i_..._r_i.E

zA -l+i " -l-i

;Z=etigisço

7-l-iJt=1--,6 / -\ / -\ -;!_ 2 2 2i=cosffJ+isinffJ=e-'r:-! a'-egeO og" rs-Ul ùtrsuJL I ax- *C ;16b::-t -r-.,

.É aer sirrs 0 a,-s! s M o ( z o)

ofvc ç.i-rr ùl.Dru af>[l t çtt r r\i i

z' -zo -sis 1t -zo).ç M'(z) ata,,,l u(z) zaa

Zt -;it.*, z -"it, 2 -zc,qosz-

-i4 -;&zc -Zo- e rx\z,c-zo)zJsàJtêt, ezc- e'3xzlJ$bs

.- { o+sU: O o:4. ,9,:')l ût:srJ\A ô.1e,a ea C:;i 6a.:;:'T,î:i:;r C iLi:tt

'u.:1 C

- \ +tl:t O 'rj(., ^ ,5iJl 6l1e,tlta A ',â 'tl 6)tê "o

C au;rl

.\tptÀt ,set ,,râ oAC e.li!| ù!i ,pnp oA - oc :a:-e

.7t"2\t ar;u oAC .' rtu ùi ê',';, ( ôi, oV) -- *,q"r,

www.mat

hsac

adem

y.net

OA-OC=AC islOt,,ït. étttô;fl,ttl rltuaziC aur;tt;ig;OA-OC 6'tel.ll ù.

.A -.LÊtlb 'rôt

Ar,.ûir^ çlt a;l.r.l .';1 oci C zt-a'u 6l ëuçtr- AC'ots4t V.O ,Lâ'tb. ,ât

t+al.r-! a;Àai é ùt'bE:l ùulll WilJl ùflÀ (!-, psô. C ahejt 'La;), -+ ---à

.( (oA;oc)--ft";a',:{JilÀÀnljl çnc) ciurtt *r:B ÀL.A:JI .t ti1 (a

acf*.ù tg.rlt çrl-,...;ib O ihi;.tl ù9ô sù B z,bul

':,6,-OCAB s{/ ùl ùçrr O

aslr.â 6,iJf yl'..,.jy! O iLûll E19,o ot B ebatSt

---) ----t.1.l9Àl é-itet OCAB çr".St Jti éptÂ OB = CA a6v"U 6'

OC - AC ,,.t1 OA - OC = AC'tg

*g ùt--U:" ùt'qlu. ùt*là 4É g)Lâl 'rjl$") ùr" OCAB ç\:lt ,JS!

.(,JiJ.t-'-

+oB-+CA r<.;",s

+CA

---->CA

www.mat

hsac

adem

y.net

r3". r"r:n":i"-1Y111

. z' - 6z +13 -0 aruU. C i{.U ctre9 err.+. gqJt (r

'pt, (o;i,i1.,-tF!le &ls:tl erltl l! u. e*tl r.{ll 6ealt ! (2

.:nigt *ls c - 4i e b - 3 + 2i, a - 3 - 2i 1q.j-lst ét C e B, A t"âttl

. C eB,Alâ;st çls-i

.71Â.91tezÔABC se\;tl Oî cr:î-V

.OABC gxa\t,pjts:" -É,.. f,):t-rJ; ev ii" -*:es ,99*lt 6. M Au rre"+" (E) É'â:le .I|(3

llffi*ù*ffi*ut11-rzM an"'vt +'ûr"i+r é1,Ê*t.(Za) gA-fr ;nzt-a 114[;;s1a

T *.,,,, çt

iii.,#i i: i, i ;.(f C) gau J! N ;sil ,,ss e*e" / lu;r .4f --

:gPt,22 -62+13-0asr4t rJ- (r

l(22 - 6z +9)+4-0 I ûrlst t z2 - 6z +13 -0 I,u,-l

z - 3 - 2i si z - 3 - -2i ti e-; (z - 3)2 = 4 - 4i2 -(2i)2,a;.ezz=3+2i e zt-3-2i:b-ô ôrLdl itslrll lrz : !j!

J(.âJt /ùt ,CeB,lfill g.r*i ï12

2ve,l 61glOABC ,*\rtt Ol ii$l v----+ ---+OC = AB ùr5 15! JaiÀe b!g\bl 61tguOAtsC

"ct.rrt ,)eS:

zÈ= za - zn - Q + 2i) - Q - zt) - tt s z ol= Zc - 4i'\.tr

www.mat

hsac

adem

y.net

fr- El1us5zo7:ZÈ'qguri ç5a OABC get2)t' ; :'

,n - t+

- lz, =|+ i' Ç) ahat ;G:Y,r.'i -q

-+:tl$lrg MO +

4ÇtM -r2,*g ll ffi + ffi + ffi* ffin= tz es'- u e (z)

.3 trr.rrâ g,orr () i.hôJl LÀtr. srrl ôrilJl c* (A),Ost

']- F * trios N;larrl in-Y ùi ùr;!'l (4

z u = 3 + i f on M z,t ;;tt e.a-v ùF lu.lbe .x = 3 ç* (lf ) a.u"

:ll.(rU ô1lsJ! ô'. f o*Ur Çl o;51'c 6jJl rlllerrl

iEt \ / -i*t- - |zN - Za - g' 2 \Zy - zç) t:.ae Z - Zçr= g z \z - zç )

]- O * tri''o N a;:'rl tn'\t ù!ô dl'u'e

,B;ya v

., tx + 3Y -12 - 0 eo ('aC) asu"

F = à'*, I2xr+3Y, -12 = ol ilr! ure (ac)l

---+MA+

: (E) eteâ+Àl ,g" (3

_+ ---|' -->MB + MC -4M{l.lu"-t)

B

M

'.\l

\\

'\ t'

szv

www.mat

hsac

adem

y.net

b-ca-c

z'-62+34- 0a,rutt .C alsrtt ùt.rri 4rsoa-,j.J- (r

, (O ti,ï) v;vll;le,rau4l ûr.rl J! y.-éu=4U s*[r ! (z

'\.fy't,.Jr tg-.tE 6;St C e B, A },Xtt 5;-,

c-7 +3isb-3-5i,a-3+5iM 6,s- M' ;t^2,\ a.ao.\ z's çilt V M ah;;:l ââ>! z ôs4

.4-2i a;-.yu eil oou;\r'ut f ,Jt*.,.jyt

I zt;.J1 6,*,ra C ;lart Oi O* Ol,.; ç z' _ z + 4 - 2i,6i ;11 _i

. 7., t*.,.;Yt,h-n

a-c' BC -2AC Als â4e9t ëÉ ABC,..ri!t ù1 è:::-t -_-

zzz - 62 + 34 = 0 ;jrbU lt- tr

À --100 - 100i2 -00i)2:so àJcu.ll oia;... Czr-3 + 5i , zr= 3 - 5i,too ,bo ùigtj. ù/- ,lô ;Jstx.U G

----_ - __f>

:,raû 3:i>ltll ,grU d! \JlÂtJ\|r.9 MM' = U :gte,.Â!t.r{rrj .r. î (2

z' = z + 4 - 2i :&e Z' - z - 4 - 2i

h-c:11 =2i ùl ùL* -va-c

_ (:-s;)- (t +zi) -4-8i -4-2i 4oi(3+si)-(7+3i) -4+2i -4-2i 20

ZC=Z,c + 4 - 2I :ot,.o^ I !rb;\lç l;sziu A6o os C atnlt

www.mat

hsac

adem

y.net

8C -2AC ;ig -.'g çs ABC É't+$ ;i gtarl ---

(È ; fi - *s(a) : | + z** "t o ft : 2i -è'et,;u r'

BC - z,oilb -'1. -Dil,:i n-^b -' - 2i ôrer-tr uÉAC - l"-"1 a-c

.BC -2AC s C iL:'rl é çse ABC ':'t,-U

t-. z z= J 2 - i "!

2 i z r = -J 3 + i .!"- z, 5 z r ;#*t !,{sJ'rl r,:3i

. Z 2 i z 1 s-tlsJl gn jlJ ô.lnca al3'Ul ;p -i 1t

z = J#2* z é'l',t 'r'r*'ll ô'r'cce alehll 6:*'t -v-!.y*zé

.,rrt?Jl Jul t]"2 éAl 'r'rr'll u'51 (2

sin 1-34 ! çes ff ,æ ê!r''l (3

dUiii; Zlsu! ôr^t9 AlJ.lJl Ûgri -i 1t

, lzl=l-.6+;l=J:+t =2:",-'t)

z, - -.li a i -rf- +. + t'l-z(cosf + iri,, f),.-,\'")

't à2tlsiJJ ô.uca a!3bll .gri 1(}

lt rl=l& - iJtl= ^lt + 2 = 2 zb'!'tr

zz= Ji - iJ z = r(+ - +;)= z ("* f i )* ;.mf â)'*,t Z é:Ll c.trll ô.u.o9 aLJhJl ëbr:-l -!J

www.mat

hsac

adem

y.net

^=A=i**r-'#=îar g(z) - arg(z ) - aryQ ) - ! * [ -- ff tz"l ;

(t) ---. z -[t#]:"osf +;sinlitr,;:r

,.\ - -Ji +i Jî+iJi--.-:--:-J2 - iJz 42 + iJz

:ùÎe.r.t (2)i(r)ù. ' sinff9

"otff,r"+Gr,,:-t(:,nry = -i(J 6 - Jt) s *' ff = -)("t-a * Ji)

,,, riord luin 2oo7)

, :-. : \û c'ititrc

(4 cm;.s;tt) (O;i,i),-çt*:.oe rct*l. fb,Jl vs-r. f.}u 69*rr.5Î

. z" - g'7 WÂ-s 6t at at B 5 zt =i W;-y dr ;bn;Jt A 6sr)

ahÀJl ôr C n .* *rtis O e,hit of.ro ,eJt ùbed r ùs*, (r

. f d)erJt'. B

.rn .f JlssrJJ 4*l irt *tt gP -i

-t--.Za=e - b êC iJ.À;)t iir:l g1 c,li -,_,

.,$+Jl JS.iJl ,)s Zç s ZB tr !t5 ti5t --"

.CiB,l.taupr-s.{(e;z) ,(n;-t),(c ;z)} ^:atr

u44t e>.)a D gus a

:613t1 çJS-ùJI ,So Z e'tS tz

-J6-Jt -Ja+Jl ._+_t

www.mat

hsac

adem

y.net

t;- D æù ?b . z r= f * li,;o aci.,r :i-y ù,i +;i -i

.ôritrfl u*ÀJ ,l!gra O i C , B ,l àa* gï ;oy -.,

D eLÀrt ô:y E ,p .z ,to .\ A zLâj/l o.,f.;c 6rJr 5*st h gS4 1t

.h6^ 4fr$ ôrl.,l dr -i

.E ât ïJt * .zB = Ji * E âlâÂrt zÂ-s oT cdi -v

.n*'vt ,1s.lr u,b dt,| ,-j't . zo- zc Z*;st r-,,,-l -l 1+

Zt- Zc

.çPg eJ}J,t &nb 6ru.,l -y

':T !l1e$;éJll &l:(jl -i (l

.É epe,sills 0 q sle M o( z s) ofvigJJl !l.1eJl :r(r!l ô1!rll|. ; f

z' -zo -sis (s - z6) ,no M'(z) uut u(z) aa( t -Æ\

l-i-ï' y :so irl.le'rJl lrôJ qirrl &ld.tl ù!s d'l'e

,2n :2rE ;57t :418-518 :rtzc=eT.zs-e'A*e-'T =e'T -e'T t

.51E l;Zs=['-l --ï-t, :61311 ç19'Àrl .bzsq6-'z

z -e r -z

-i4È _- o -zc-çt;t?-ii :,Jl+rt JirJt ,Sezçat6Oz2

.Jr..ill ,!ûl ,c it B , A !^t.tl ,),j; -o

t;. z o- * + * i.oo D ,L-â.tt âÂ''Y ùi ûlj! -i (2

z,a

Ul;z) ,(n;-t),(c;z)] *,t, u.7t s7* slD D

www.mat

hsac

adem

y.net

,,-=3#=.=fi.*Li,..tgtt .rg .D igirlt .J:r; O

:ôr5tJt u-ô,)1.# D i C, B. lâi$ ù1 ù!ôrJ _

oo -lz ol - 1 i o c -lz rl - r, oa -lz rl - r, oA -lzel = Ltr.r

r^rJLa .;éi9O:Lî'rl tàjsr. ('rl ôJJlJl u-À J! rrp:;; D iC ,B,A&St ,351

,h 5tottS aé"!t ;ju*rt -î (g

.1l1 osr gfrre k +, -ts M o(z o) oflr,9,ut fts.rl, ;rç'lt rr.;t, rrj iz' -z', - li (z - z r,,\'e M'{z) ;;^'t1 14 (7) ;

7' - 2s - i ,,s;i z' -z u- 2(z -z u) ,ç 9r,,rJt

l.hj aisru ôtliJt ù!ô 4.1çe

tzE-13 ooEaull an yù1 ûu!_?

= .l-3 ,o;^9 z'zE

;4=e"3

r-11 r \-2zo-i=zl . +|il-i

')

_(f.+,)-(+-+,)(+-+,)

=i.*,

-22 - i :l:t.tt

Zo- zczt- zc

CD=CE zus

,?- z:-a,*tu,-tt,,e -i (a

'E-.c

,CDE ," rtLt,&::b gk r*t -r-,

-, . lz^-z-l co .

-r 9 | u v l__ :r{{rlza-zcl cE

{J-

is, r.'T-t'

:18

CJ

arg(s'z )-+ s arg'5

www.mat

hsac

adem

y.net

ët âr'*-cDElËu :::. - tT-fBl:T J o

lroLB\-

-':*-

li -/t iCY

---.1'

.22 - 42 +8 -0:ilrlr$.C i.!U rtarll &9o9.. é.,.t- tt

z -1, Z $2a sJ' !15 &J ùo'G:* s9'r- 4S P;'q, (Z

P(z) - 23 * QJi - +)

" + (t - sJi), + ftJi

. r(- zJi),,',.-r t

'b-rZ. t5:. s,re ,J5 &J O".ersf c a b, a a4ri"Sl rlJtl'l iÉt -Y'

P{z)=(z +z^11)(az2 +bz + c)

P(z)-o'a'u.Ce.&-+, ++\.(O;l,i) nq'JJ, .rrr-dl fl"$ d! \J. r-41 '=52f1 çg*U Ç

(r

:r.-..ijll ,r[c k!-le' çrl C i B ' A zJal:St 4'i

' zc=-2J1 s zn=2-2i' zA=2 +2i

ÉIi"u"" )"otoot t"t)

. C iB,AJ^Htës-i i

www.mat

hsac

adem

y.net

. ;,- 4 .:r r ; O uç* ra (C)ô.rrur .J.ô db !- C i B. A :j &

a,_rf:L ùtrst/! t-+a êt:-le Zs s z1;{:Ll ù,,rrrrl ù. ,5, ôr^r df -<.++IOB;OA)

asr;u .r"r'* f; oî eu-r, ( d;Cî1+r,i, ùqùbl{ r-.i ii' -ù

trd;Èl' tanf; = | + Jl'ûd''' --ô

#lsil, z2 - 4z +B=0 arrutt ,Jt--i (r

A,=-16 -16i2 -(4i)2 lgôrtr$ oJo .r:.ce J.zz=2+2i s zr-2-2it6 ù$lj" ù|- rl.ô â,:t4t O

/ -\r(-zJi)-o, e(- zJi)r7L.z-i (2

tcab,a&é-v:ôlttll gpl ,grr! .J*:-.i Cab,a W'c,l

.f.rSÀ id.r,9- - Z*,.À)l 1:.isl9; - û\t l-tl âÀtÀ.

C=8 s b=-4.a=1,.r.u

r(z) = (z + zJi)1 "' - +, + 8 ) :thr!.g

,p(z)-O ôsl*U rJg- -z

r() - (z + z.l1)( z'z - 4 z + 8) t4t

I z +2J, -O :4i.e

Lz'-42+8-0zo=-ZJiz F 2 -2i,a P(z) - 0 all'tt tlg,b 61 c':';zz=2+2i

www.mat

hsac

adem

y.net

<É,a jÈl.C i B.lld ?.ti -''r

zO t;ilreil(C) ôr*^tt,È ë' e C i B.l oî or+ *

oc :lz.l: zJ-z 5 oB -lz "l- z-ti on -lz nl - 2Jl,Qtt

.Q1_Qfr _QÇ za;ae

.zJi 'n+.. r 'r O rof.r. ç;rr (C) a;ru & tp C 5 8 ,,,4 ûiitr 'ù:l

t Z 6 s Z1U çJlJ ô.t"or llÉtÛ -q

lznl-ZJ|.1aqe z1=2 +2i ,t4,tt

zA=2 +zi =rn(+ . $i)=zJl(cosf; + isinf; )'*,zB=2-2i = 2n zl:o-r.l9

.zs Jô.ta.e -&Siezn) a,r^"ff0i 6^:-;,-+ +.

'(OÉ: Oi) ô-sl'u ùlrrlrLt u.f gu"-r O

'(dtù)celi! ùUùbrtt e-ïô lrF-), --,

-?. ,

-> ->.BA ,yflt,J.ir ùL'.'.t ( CB ;CA ) sIOA ; OA)Jlu,-st)r

(&jsil !À,ej ÉeL"i i*h.e*D (d ; ch = I ( d ; Oi1 = 2 .^- t' z' +

---+ -.>

-_".' +à.!.:,. aielj ( CII ; C À) s e-ÉJ. asr) IOB : OA )

,(fr; È) t rtyt "a *f; at su,-ro

tÇ =l z s - 211=l- zJi - z - zil -,[Ç z^li -f * 1. zf ,o-u,

www.mat

hsac

adem

y.net

sç =lzr- zsl-l-zJT -z +ul-,*: ft 4 s ;t-Éutr 6eua CAB ÊJitl ù!i r!:tt'p AC = B C.a;'e

:;1i g.:;:-; 7[ grL+ ,..rrll l?l9j g-9.c3,.,;':19 , (d;ùUttt,+-+

\CB ;CA ) + \ AC ; AB )+\BA; BC )-rE

\AC; AB )-\BA;BC )6t

,-zf,+(z)2

( È' ô = +G - (d ;zitt = l(" - ft)= {.*', + -----)r iæ

.\ AC ; AB )csli! ,J..t so f : j::

, tanf; -t + Ji ;,i.,""i-,r --o

t, = fu#L - 2 go I ahal ai'v .[,qa] â.Àilt.j,â:r"' 1 ûsrr

6e. es !.otsÀJt 1n,aa gl (Cf ) p,n*tt JF IA= IB e çtr - çg ù1 *e

.1 ,i Éli CAI e$t si n:u; [,la] a.eau

tun(z.i:Ê)-#,,,

AI -lzr -zdl=2s CI -lzr-zcl=2+2Jiu-l:e

tun ( È; ù = # =ry= I + JZ :*!rrLg

, ---> ----}t 2r( it, n) +llt r.* s" f aÎ ûur. e 4rJr Jr3; ,.r.g

.tan{-r+JT,;ic:.;

www.mat

hsac

adem

y.net

[=.--****.111Y3

ze z *.1)ctji:eu re"ra # P(z) g -t

P(z)-s3 +qJi zz +242+24Ê

Z $2a ss.lS ,.ç1 O. .a;i ,gi"u 1t

PQ)-(z +2Ji)(z' +zJi z +n)zz + zJi z +12 = 0 :ôst*[l . C +5;r slæilt àcane,r ,2 ,b Q

'P(z)= I alt-'lt C é ..lsl''l ë',:-l (3

. --)--à, (O ; i ,i ) ,r-q"fle ukrU pl*[l ,Jl Vs.*.fl r=$[l 6ea[l gi -rt

:\+tl Jt rg-tg gttC s B , AJoa;Jl 7cz;

zc=-^!-l -3i g zb --J1+3i , ze=-2Ji

.É*itf ,JS,àJ| ,bzc s zn, zAirâ\S vft (l

www.mat

hsac

adem

y.net

- 4 c,'jr;g O as;t€É.,!Ér 4rrrr It,j(J-'.R Or+t irÉg i,t<lr .uci

.8".o R Or1srrÉd6r 6ï 4 _r1

.Rùtprtt, B irr D ebnlJl;irll .6antl JlS,iJl dle.\/-,'l -â

.[co] "r.t,,1

;;r"rl (l),;s'r tr

.(l) a;ru f* ç o au:.r 61 6i'o -i

.CBDy CAD ûilill ù. .JS L..h êa,-1, (f) ,J! Oq"r B , ACl"t t Oi ,* -v

zJJlzI s)l

, PQ)-(z +zJi)(t' *zJi z +D) , C v z ,.s ç1 s. .a;î éi'.u (r

(, +zJl)(r' +zJl z +n)_ ---= P(") :c. ,1. z ,)s tz1 ,y

z2 +2Jl z +12-0zutuJt J> eA,--36 -36i2 -(ei)z ,eoôrrr$ oil;.e.. O

zz=-J1 +3i 5 zr--11 -r:r+oq4goùl-..J.rtaJst*tl O

t,5*'trt .5.ltt 4o zlatS C 1t

zt - 28 ein''ug zn - -2Jl zv,-ts

. tç*'trl Jt ùJl {jt Zu a4S O

P\z) -g:ôrl*'!l çl= (3

{':'!':o ,^ ^'*, (z+zJj)("'*zJl z+n)- o'ra'tLz'+243 z+12-0

( zo=-2Ji 'ç P(z)-gu,:tsll Jgr' 3Ï c:::;I ,'--JT-tilz'r--J1+zi iI s)l

,"=t n(-T,.$i)=z.lt J+ ,*ez, - -"6+3i 'q.r.r

www.mat

hsac

adem

y.net

-1r"- lgJlât r*zc4sO

zr=z.l-t( - I-4;)= zJl s iT'*, z. --J3 - gi'q.,r- \ z z )

,Rùlis.lrÀsil é.tlsJl J(2

,J* .9r.gJûte 0 a:,-el3 Mr("J 0151e,gi..ll !l.1e.dl;r5rtl tr'rlt,72!t:

z' -zo -e'e ç7 - zo),r+ M'(z)zta M(z) zta

, -i4 (- l; \z =e -.2-l+-+i lz,soRùbsrllafitl a,t;(tl ù!id.Ite

\z z)'8,,o R 669.rtt A 4eo ;;l ;1tts -u

:dUlie R ùbeJr! A ô:* A' ô5;)

_i* _ir _ ;(-i*") _;TzA, -;'3 .z,t=e'3 xzJi ein=2J'" ' ' ' -2^tle'T

ç XçtXp _) r-| lc+lp -\- 2--

.B oo R 3l.p.rtt, ,4 à;ec 6l çl zn, = Zs t!5!

:qs-ll r,F.all é'e D âhâll eÀ'9 z D 46 -q

:ù!s R ùbgJq I ô.re,é (,À D ùl ti

-0

-Jj -zi+-Ji +ti-Q-7o:6çi'ai"tb

. (r) arrurt gr. ,o o ahi:lt :,;s1

' (f) g1 g'.'''" I e I qui:ll ùl ù$ -r.'

----

" " =(+- *)'" =(+- *') F.ri.'4= rl + 3i

,(t)i;r.,.rrgr. eO auz;ttgl g,.ll -l 1r

- f,'r f - o {co] +t.,r r-i,a:ro sir.u! eræ

-3+3

www.mat

hsac

adem

y.net

N -lzrl-zoa -lz rl- 2.fi s oÀ:lzrl:l$

.(f) a;u.'r g1 6ro"rB sA;j&j,gs1 . OA-OB:OC {ag''CBD eCAD 6:t:lt ù. elS:-.:L dhz.lO

ùilill ù!Â (Jur,.g. [CA] r"rbg sJl ôjl4I ,11 3t":r Be l;uei;l.*;tt Js B s I 5! OUtl ;tw 6 CBD s CAD

z' - 6z + l0 - 0 t z i.l5gtl ù'S eJotrtl C arr,.+tl é Jlr (r

:!16 Z !.çr^ r.re .tS .t-j a" , ir-ll s9r*,ll t5 p ùS1| (2

p(z)-23 -t222 +462-60

B

iln**,o"tïï'*t"

www.mat

hsac

adem

y.net

'P{a)""t:z r.l. :r rre J5 J4 ,* e=c ib . a -a+.>ltatle!Jt ,ie -r.'

p(z)=(z-o\az2+bz+c)

'P(z)=0 asel C é ..l- -€

e , @;î,i) r;.il+.e rôls. fL" é! .-.,. s*tl :6tl '5rÊ-tl é (l

.\.irtll J" 6 i3-i,3+lasrft rlJ'lrl r,,"C iB'AJeïJl

.C i B,AJ&t ë'-i.7\a1 ,9-3te:ÔACB çrtr.rtt ûi cdi.V

.OACB 7l,z\t,rjleb a'..b ét1t-'le ' OB iOA ql5^hll ,.19 ieu -:

,z'- 6z +70 - 0 art'll J' (l

6=4 -(2i)2 ,,eÀ À,ùls.!l oi.o;., O

zz= 3 - i it z f 3 + i'vg'li'glJ" ù'l- J'ô ;J;tgtl O

p(6)-o.P(s)vt'"c'1Q

:c 9b . a At+Jl ôlJtirl .t ti -V

;.rr., y.rsr /.-*rl9'- 91i'c..,J tl !.rlgt sl Ô!.çll eÀtb' aôJ'b tjt":''b

p(z)=(z-ù(r'-62+rc):!s!' c=10 s b--6 ' a-r:p(z)=}Us$t 1)e -a

zz=3 - i g zF3 + i, zs - 6 :ç p(z)= 0 a,sktt Jel'

.Js.rjl J!Ûl ,c iB,Atxst,Jé6 -l (r

z7\ai 6,lrguOACB eeb.rl ùl Ûç! -Y

' zç -à, = 3 a i' Ed gt*Jt eô'\, z A - z o = 3 + i, 6l {"-'st zs-s

' l:.gruai 63tç,,OACBçt)rtt Jti t)auedl=Eë';ie:u

www.mat

hsac

adem

y.net

or -lz"-zol-ll-;l= Jro ; oA =Pt -zol-p + l-Jb +,.,

-OA:OB.us.OACB 7:/"Ë9' €jbr. er,.b Gb=-l

OACB gwistg.ils:" ç:el ù!s rjtrl,g AB =2 e OC=6ztb-$

.;rt* OACB ç\1t 6i ,gl';.ùf-li:. rtv

A-^_

o -\-\- -/-a X---=---/

B

' @ ;i,û &el,-e l.l*r Pk'o J! :s*' .ee:*tl

B, A ;J s, z z- | + i Jj i z f Jl + i Jî:.rt(il,J,rr&rl r':'j

. ., (rU g9r*ll é ':.aljJl ste lôôllJs,

. zz i zl o" rJSJ s!:fl JS,iJl ùt (l

.Z -?+q).brez ds4e

ùbs.rjl qsl.j. 0 {9li! ùqùlrq t..E èr:.,1 Ê.,r irl JS.tJl ,+ Z él.B Jl A J'e-3 O a.u or5.',r 6JJl

.g.r:+tt J53r ,J" çS c;tltt ,15.t'St 4o Z -St -i 1t

- 7f- lt -' sm Ë t cos17 V;+'g Cijiirr -'-'

www.mat

hsac

adem

y.net

2&l: Zl srrl, ùiEll JF.àI (l

l",l=lJi * iaÈ .[çrrf .W - 2,,a.d

zrfi+iJi=,(*.,*)='(*'

t zz

k,l = lt +i.61 = frffi - 2:'14,r

zz= | +, a = r(-I* tf )=

r(*. * + ;,io g )'*,

:eiV iail ,pZ ars P

zài i4 -i4 i*-:1=€

r xe * =e '"zàa

:!l.;guJl qglj gtt::.,l O

çÉ opr 6jJle 0 qel3 M oQ o) oft6iltl ùbeJr, !(.ltl ô)li'Jl ; f

z' -zo-sio 17 -zo)'a M'(z) '*"1 M(z) u;;

.t:-o oF B ,lt A .E rr 0 qglss O Â!n:Jl 0151r .;l.prlt tJo .;l k9

/-"i#,sr,7 ="" .*,zz=€io zt,,ê'c!\

e = ff,;,sr

S + isin #,"*' Js.lJt sl' Z qts -\ tt

Z1

\

= cos ît 12

www.mat

hsac

adem

y.netI cos

'4

ltD: slll

(r) ....... Z -cos# + isin

| *" ,+r=#:!i c:::; . à.Àr. ir.b (2) e (r)

[.i"ff=G;0

| - i.

v-'à-

www.mat

hsac

adem

y.net

6-:tt tt'"reÉ"i

-| /-\- I - z + | - 0' (.8) asufr . C afrft strrlyr ereÊ+. É .J. -i tr

.*\tt.1c.tt ols ilsl*.U oia olr u,c !s Ét -y

. z4 - zz * I = 0, (A') aouU Jg E;,:_,1 __7

..rwill JS.iJl ob ôcGll oj.ô y'.' (J,. )15 r;5t -r-r

, ++\,lO;U ,v ).,-l+rlle J,cr-dl fls.U r.J! Vs*lt r-.5:tl U$-tl é (z

',,1? (E ) âJsÉtt Jeb se D e, C, B, A lt:l ç.;

-Ré(z)>0 sRé("r)ro . Ré(zr)>0 , Ré(zn)>o

. D e C ,8, Al.t;tt çt" -l

ABCD ç\:sr a.r:L t& -v

,,_f à,t , 11. Zt =* -iI:À{ll r|.trYl $'j'zz

. Z | , t.ftll s.t*ll ô.tc9 {lteLJl ùe (l

.zz= zt:31 ;!.e q3lt ,JSàJI ë'ez2 \{ll r.*11 ,+51 -i (2

. z z VTrll r.r*ll ,s."irl JlS.iJl ù,iç -,-,

.g*+rl JÉtJl ,* zsé:Lt ùJdl :n51 (3

Z = ZzXZl.-' ltr.*ll ! (.rll trsll Z JS4 @

.Z é-*l o.rrll ô.r.o.eg aqgel ..,,,-t -1

.,ft+Jl ÉrJ' ,ttr Z é-J,l r.s..ll r;51 -çr

1l ,tr'cosTi r cosfii".e èpiat-'>

2+i3-i

**-*"*.t=t*1'**"

www.mat

hsac

adem

y.netzl s)l

: t Z 'r'7t- ôr, !r5 &J ù. ' àr-^ 4.r- 55 P 6,{t

P(z\-23 -zz -22-12'P(:)Y"-t-1o

:Lu-t) ,2 t S9 c.r" J5 .J-J o. e.ar.r c i b , a Z'À'Â-)l rlrt'll ûi'9 -Y

P(z)-(z-6)(az2 +bz +c).22 +22+4=0a1ùg.lt . C;t1[l st.rôt aca.4o ,2,,b -i (2

. P(z) - 0 ;atcutl ,,Jer- g:::-l -ur

zII s)l, ++\

e ,(O;i ,n ) n]9'd4'tt,!.ls-U fl.*t' l! -r--r.3'*tl ,r{fl çealt é

;\.fj,l Jrtèi-'etdrl D i C,B,A$)Jl_zi4

^. I^ _ .t -''1 _ , : Ii.zo=3 e zc-3-3t{3 . ze=2e t, zA=l+iv:.ç:J4l Jt i.Jl ,,)t 4l ê zd{}l r.r*ll ô.rnca Âle.hll Y..,-l -Î (l

'g+?Jl Ji'Jl & za étll u*Jl r*'51 -çr

.D i, C , B, Al"t:tt çb -i 1z

.AB CD ç\!t es'.b,ë,;;;zt'-7

-|È,;;,*.'"+DC

-- 1.,ane sePt 2oo7 sTl)

iRar '4 '" - .' ---

- 6z + l0 - 0 uùl*U . C a.sJll rl.rirt àca*3" é ..J- (l

www.mat

hsac

adem

y.net

.1 Z ..'St' e,.,16 .,12i 6,. ' irr-- s9,e rF P ùq, (2

P(z)-7t -1222 +462-60

'P(O)...'"-t -i

:\tJ, Z Ç2asrr.JS J-j e,4c ib,a aa;',tlùlJtirl ûb-.,,

P(z)=(z-6)(az2 +bz +c)

. P(z)- g';1"1*l .C é.J- -+, --5--\

'@;n,n ),*t":tle J'l'rll ftstt ,;1 .."-tt' vS$ çe:*tt $ (r

.6 e 3-i,3+i:\.iiJl ,,,l"kf-leJ dt C gB,AS"xStç';

.C eB,AJ"ÂttëD-t

.gl,al .e;lel. OACB g!./l OT & -v

.OACB glLàll ,tjlsr. gt Eeu.le OB. OA ùtshJt qt ù.J15 -q

.(O;i,i)|,4,We .r.oh:r grra l! r-,. e,-:,c ,gs;*[l

.22 -22 +4 = 0 a;utt C a.fJtt ùlJrll arj,ôe,. é !r' (t

' zs=l-iJj 5 zn- l-iJi &s, B i A æbâ;rt\4u ,rer*t' É *; tz

' \.itl Jt loÀUi-Y

.ç'i,'yl ,JÉôJl .Jr çS .d:rr Jsâl èc z B i zAgr lt5 l,.51 J

.Bi A;ç1";;:t{-9

. g,l! Il4t ?iJeJi',É aer çJl ., (rll ,geuU é G,hôJl ,J,j*rJl R é; (3

z' - e4.z ,r:< z' ai',t)l ûti M' â,hÂ:Jl , z eâ'\)l

www.mat

hsac

adem

y.net

-R+-s"al

. K ,,lfJ,*rrl,l Zaa;l6,4orflC a y; -9|'J',rtf 4J5,à ÈË-t i . C iÀÂ:Jt 'éi.y zc ..1.)lt ùJrlr r,iÏ J(.ÊJt de _

.C aÈu $ _+

,ABC 3 t'$t;-r:L t".R,!_cdrbC ebjr,lssy * B ;uu,iÎ 6, _r

.(O;i,û dr+:. g r.l':. Ê&. *l! vc.ac ,99r-,lt

..lgtJt Jo z' i zqSlt r,is'lal' Ç:* M' i M qtalr a;r,t

.z,Â*t"lr,,,i y' i x', y, x &9 z' = x' + iy' i z - x * iy rea:ù ,l , -l ------)- -.+l(e\Z .z)- 0:ù5 l5l L;ôe li! rjt.r,ot'''c OIrI' i OI,[ qrb-i.I;1 ù-ôr (l

:!15 ts! àÂie tS! ôr,te a.u:.,l ,* M' i M, O l"t;stùi Oar (z

- ( r-\Im\z'.2)-0

. 22 -laÀ,!u ûrs ahÂd N (3

+ ----->ON i OM ùtele..iJt ù9Sd ilg, ç9:*$ U M hùJt e.canar o-o b

!!r,rfoll iâ

. I-t ;j,yl ùts :alan;Jt p . z * 0 ûl &r;'., (4

/ \, . I t2

I 4-t \ A l= -z'l+-;,aic-:r.i\2. | , l"'l-P i N, O l";tll ùeÉ e..e., z aiettJ l ûlt M hbJtâlaq.o èr:-t -l1

. +li-t s5

www.mat

hsac

adem

y.net. (O ;i,i)

";1"-e r,[r'^ el'. c!!

'-,. e"*ô 6er*U

za= L+ i , ze = 4 + i e4!l sl.rrirl ri,ê D i C . B . A uat a7:

:.Fgt,)*zo--3-i i zc=5i

.DiC,B,,4àirtl eie(l

, z eÂ,\)l o$ M âJ.Ë É aef a*iu $ ,5e:,..1 llâUl ;3ztSl f & <z

s' - (t +zi)z - 2 - 4i'Q z' âl'l.Jt ûts M' ahÂrJl

. f ,t-4\ B e A 41"ôrJt é.rs," ,lr -i

.t€ii'\l ùÉ'i *,r r', Ç2 ôroLa ôJ.tl9 ahij & f ,kgl,trl Ol c{Î -V

.z' - z = -2i(2 - i - z) rz vSv s.r .,5 .J-J ù" a;i cr^r -Î 1r

^

tf i.'f 'ùqsltq |..+i ffi -1, Ç2 ç,*;s M ahÀr .Js &j 3.c.6:::.,1 -!1

@â: ffi').'"t'1çlMM'eJ*l ar.^b L -€

. z. - -l - i"b;.i'YJl c,l! ahill Z 35:t -c

.,5r'Vt .15'alt ,7e Zt '.St t

. f &r{llb. E Àbâ;Jl \eo E' aa;:sl t z;i I

' (O;i,"1,*$:r e r'cr-i^ 9'r*" !! 9e""c çe:-Ir

f*I"-t*"";î"-":1''

zc = zr it z n= 5 - 2i, zt- 3 t$-lst Gil C e B' A $dl r'sù (r

www.mat

hsac

adem

y.net

(B 5A6e ';t '. M 1 zt5;>',t ss;-Ut?Ælf #.Â-_fl. 45U És' =.: eJE.,{BCé.EU ùi c-ii-l

. t = ? =, çSl r,r.*ll ô.r.o.ce a!3'hll r1rr.c./i -1;z-5+2i' '

-al.Â:b ls.rc =*

l* ë19a z eô'lJ,JJ c;l't M Jaâ;Jl ican3c ,jc --z-)+zt.qL,

. 2 - i e;-wt ûts ah.ùJt Cr, AB C,".ritu ah..lt ôttJjl (C) ûsr, (2

. _ I *-rr:, Çl i.h.i:rt .,j(r^,e.jJt R ùbeJJ a4{t ;{{5jt,hrt -i

.(c') i;rrl Ç1rÉ_: Ârrr* ..sr .R;5eu, (c) ir,- (C') d: -v

.(O;i,v1g*ti*e r.t*. e!'. J! t e,"b ('$*tl

p(")- z3 - 622 +l2z -16zgai, z é,.s.rs .l5,pi go

'P(4)-,*..rJtr:Z ,..1:a s,*,.lS,l*i O" e,:p.f C! ô ùfr" oiùrr.iÊ -r.;

, ,t .} \p(z) -(z - 4)\z' + bz + c)

p(z)-0,atuu C arr,.+U g,b -i (2

.v:l:U JK,ôJI ote ô.:l*Âl o.rs ç!9b l.51 -ur

, (o ti,v) *;1"-e J.tr:. f,rr. J! vs*tl r-.':lt de:.&tt é (g

zc-I+iJi iza-4,2a-l-i^11 ç..tg 6trC e B , A l.zu a:,:

.C , B ,A gi:,t ere -1

.gwist u.-ta. ABC eeo..l Oi cdî -v

.ABC e"v,g e,t ,,4e b*a yt -+

www.mat

hsac

adem

y.net

( Bæ S Nouvdle Calâlonie uarsâl2)

: :r+ P(Z) r_l-Jt ;$S , C i.S. -2.!l rl-lcYl i-c .^- s-a , É*. ( IP (z) - 73 - (z + i Ji) z' + z$ + i Ji) z - 2i J,

. P(z)-o 4!lJld- I zo*i.ti,,<fl.u'JlûiÉ(l; L-.ri , 2 c-É. -.,;a .:.lo ,JS .J+l ,-r . drF.f Z, 3 a igi-riJl Uirr'll de (2

pk)-k -iJ2)(zz+ "z+b). P(z)=o : irLJl a .,r J- (3

,(o;i,v)oÉLrillrs."l-iJl ,lJl Jl ','r"r ll .,<JFjl çrôJl é(II, Za=l-i, q-I+i:ter-l:lél K s J , B, A'. Litl! Jii*j

'3n' zx=e'T s z1 -i^fj

.tis)ils.l,ll .Xxl +û1 ,*K-:J,B,4!Â:ll pl'(1

Zr=-li çÀ t 13=) ùi ù! . K :L;dl J i-'-i1-, / â.,lâr I ùSi (2

ir+.i,,Jl.*çll 6JilJl L*iiJl ç-J.!l L s J , B . A Li-Jl ûi û#(3lÂ-r,tâ'; tJLÀ5-1"

O "-f+"ç!l R ûl)Jl -É;. zo--!+i r61;-Yél ilijil D ûSil(4

' D ')l "I cJ;r1 çrll3. ft rrlJjill fullj.tb -l

. R ùl::$ t â.tiill ity- C a.talt âi=) cro -.+.(é]5..t+! &)t enCO 4t+-!t++uu(S

t fo,,r,'"'"1""1Ïl

-(O;i ,n ).r-t+"r acl* çt*c rJ! vg"'" ':6tl Éer''[t

r 5,, r tl: d2)tt */l

. ùf.i*ie' Jl.rebiaJyZ--a*ià:-,é1'll ç52t1 r.r*Jl Z;Sl

2 -a-ib::lifll ':sil rr.*,1 Jl7 +Yi

www.mat

hsac

adem

y.net

E -r.7. z's z cf:.0:r*ur*lù..6tiÊ

. V :e) ,ler*. r: n {,r+ sro,.1É.I:t 6..a;î;!

:4Al 'Al.ée se Z ,L- za - -4.(E) atr+r ar',i

(.E) aor'"1 ,bZ s-zuvs.iF(E) ask"Jl-2,;srs1 o;l 40- z o= | + i ,={tl s.nr 3cri G)

. ,5,ttt .1s-t tt So z o ,-,st -l

. (A) atr."l ,J- z o itl éÂ,ir -r/

. (f ) arr'"1 6É!l .lel' Âtu,l ùôlJl cdl3,*tl ù" cu-l (D

zé,llJl s)l,g;tl rJs ttÂ.|, tJ:'ll 8/t D s C, B, A è*J

-zo=l- i e zç - -l- i, zs=-l+ i' zu -1 a i

. rR ùbeJLf B ebûJtUen Eç.-., .- * qtt:tc oile igJl ùlrer,lRùsJJ

.R ùl:grru D i.r:,. F

.R ùr.r*rr +çrfr a|5lr 69 O

. zs -l + JT,?E açlr a;-v,3i ;;1 J €)

. F at"a;t âé_! zF tb _v

.sfaie ste ga 'A - tE ,l,-.âtl \JêV Ol Ou -*- z,l, - zF

.F t E , A JIïJJ a*..rL e:ir-i ls l^ -!

.,1s;tt 6 E ahÂr,l Jr. -

Documents

Bac Complexes3imbac lak