12.2 Phng phap anh phc

Moi ai lng ieu hoa se c bieu dien bang 1 so phc (anh phc)

2.2.1 So phc

Mot so phc C co the c bieu dien di cac dang sau:

j: n v ao j 2 = -1

a: La phan thc cua so phc a= ReC Re: Real

b: La phan ao cua so phc b= ImC Im: Imaginary

C a jb

V du: C = 6 + j8.

6: La phan thc cua so phc C

8: La phan ao cua so phc C

Dang ai so

C = a + jb (Descartes) th C co the bieu dien dang cc la:

Dang cc

C C

2 2

cos

sin

C m

C a b

a C

b C

barctg

a

Vi la oun

=

=

=

la argument hay goc

C = a + jb

Dang lng giac

Cong thc Euler

eJ = cos + jsin

Dang Mu:

A = a + jb = C (cos + jsin) = C eJ

Cac phep tnh ve so phc.

C1 = a1 + jb1.

C2 = a2 + jb2.

Phep cong: C1 + C2 = (a1 + a2) + (b1 + b2)j

Phep tr: C1 - C2 = (a1 - a2) + (b1 - b2)j

Phep nhan:C1.C2 = (a1a2 - b1b2) + (b1a2 + a1b2)j

Phep chia :

2

C

C1 1 2 1 2 1 2 1 2

22 2 2

(a a b b ) + (b a - a b )j=

a + b

5 Phep nhan, phep chia dung dang cc:

1 1 1 1 1

2 2 2 2 2

1 2 1 2 1 2

111 2

2 2

C a jb C

C a jb C

C C C C

CC

C C

V du

72.2.2 Bieu dien ai lng ieu hoa bang so phc.

( ) sin( ) ( )

( ) sin( ) ( )

( ) sin( ) ( )

( ) sin( ) ( )

m i m i

m u m u

m e m e

m j m j

ai lng ieu hoa ai lng phc

i t I t I I A

u t U t U U V

e t E t E E V

j t J t J j A

V du

Cach s dung may tnh e chuyen oi So Phc (Casio FX 500MS, fx570ES)

Pol ( 6 , 8 ) = 10

Ket qua

Alpha tan = 53,1

6 + 8j = 10/53,10

Chuyen oi dang Descartes sang dang cc

10/53,10= 6 + 8j

10 shitf - 53,1 = 6

Ket qua

shift [( = 8

Chuyen oi dang cc sang dang Descartes

May tnh Casio fx 570MS

03 4 5 53,13j

Chuyen sang ON - CPLX

Chuyen oi dang Descartes sang dang cc

May tnh Casio fx 570ES

Chuyen may tnh sang tnh toan so phc: MODE - 2 - CMPLX

Chuyen oi dang cc sang dang Descartes

Chuyen oi dang Descartes sang dang cc

The set of equations can be arranged in matrix form, as shownin equation A.6.

HE 2 PHNG TRNH

11 12 1 1

21 22 2 2

a a b

a a b

x

x

11 12

11 22 12 21

21 22

det ( )a a

A a a a aa a

AP DUNG NH LUAT CRAMER

HE 3 PHNG TRNH

1 111 12 13

21 22 23 2 2

31 32 33 3 3

x ba a a

a a a x b

a a a x b

P847 Fundermantal of Electric circuit

1 12 13

2 22 23

3 32 331 det( )

b a a

b a a

b a ax

A

11 1 13

21 2 23

31 3 332 det( )

a b a

a b a

a b ax

A

11 12 1

21 22 2

31 32 33 det( )

a a b

a a b

a a bx

A