So phc

Tran S TungTran S Tung

So phc

1. Khai niem so phc

( Tap hp so phc: C

( So phc (dang ai so) :

(a, b, a la phan thc, b la phan ao, i la n v ao, i2 = 1)

( z la so thc ( phan ao cua z bang 0 (b = 0)

z la thuan ao ( phan thc cua z bang 0 (a = 0)

So 0 va la so thc va la so ao.

( Hai so phc bang nhau:

2. Bieu dien hnh hoc: So phc z = a + bi (a, b c bieu dien bi iem M(a; b) hay bi trong mp(Oxy) (mp phc)

3. Cong va tr so phc:

( (

( So oi cua z = a + bi la z = a bi

( bieu dien z, bieu dien z' th bieu dien z + z va bieu dien z z.4. Nhan hai so phc :

(

(

5. So phc lien hp cua so phc z = a + bi la

( ;

( z la so thc ( ; z la so ao (

6. Moun cua so phc : z = a + bi

(

(

(

(

(

7. Chia hai so phc:

( (z ( 0)

(

(

8. Can bac hai cua so phc:

( la can bac hai cua so phc ( (

( w = 0 co ung 1 can bac hai la z = 0

( w co ung hai can bac hai oi nhau

( Hai can bac hai cua a > 0 la

( Hai can bac hai cua a < 0 la

9. Phng trnh bac hai Az2 + Bz + C = 0 (*) (A, B, C la cac so phc cho trc, A ).

( : (*) co hai nghiem phan biet , ( la 1 can bac hai cua ()

( : (*) co 1 nghiem kep:

Chu y: Neu z0 ( C la mot nghiem cua (*) th cung la mot nghiem cua (*).

10. Dang lng giac cua so phc:

( (r > 0) la dang lng giac cua z = a + bi (z ( 0)

( ( la mot acgumen cua z,

(

11. Nhan, chia so phc di dang lng giac

Cho :

(

(

12. Cong thc Moavr:

( ,()

(

13. Can bac hai cua so phc di dang lng giac:

( So phc (r > 0) co hai can bac hai la:

( M rong: So phc (r > 0) co n can bac n la:

VAN E 1: Thc hien cac phep toan cong tr nhan chia Ap dung cac quy tac cong, tr, nhan, chia hai so phc, can bac hai cua so phc.

Chu y cac tnh chat giao hoan, ket hp oi vi cac phep toan cong va nhan.

Bai 1. Tm phan thc va phan ao cua cac so phc sau:

a)

b)

c)

d)

e)

f)

g)

h)

i)

k)

l)

m)

o)

p)

q)

Bai 2. Thc hien cac phep toan sau:

a)

b)

c)

d)

e)

f)

g)

h)

i)

Bai 3. Cho so phc . Tm phan thc va phan ao cua cac so phc sau:

a)

b)

Bai 4. Phan tch thanh nhan t, vi a, b, c ( R:

a)

b)

c)

d)

e)

f)

g)

h)

Bai 5. Tm can bac hai cua so phc:

a)

b)

c)

d)

e)

f)

g)

h)

i)

k)

l)

m)

VAN E 2: Giai phng trnh tren tap so phc

Gia s z = x + yi. Giai cac phng trnh an z la tm x, y thoa man phng trnh.Bai 1. Giai cac phng trnh sau (an z):

a)

b)

c)

d)

e)

f)

g)

h)

i)

k)

l)

m)

o)

p)

q)

r)

Bai 2. Giai cac phng trnh sau (an x):

a)

b)

c)

d)

e)

f)

g)

h)

i)

k)

l)

m)

o)

p)

Bai 3. Tm hai so biet tong va tch cua chung lan lt la:

a)

b)

Bai 4. Tm phng trnh bac hai vi he so thc nhan ( lam nghiem:

a)

b)

c)

d)

e)

f)

g)

h)

i)

Bai 5. Tm tham so m e moi phng trnh sau ay co hai nghiem z1, z2 thoa man ieu kien a ch ra:

a)

b)

c)

Bai 6. Cho la hai nghiem cua phng trnh . Tnh gia tr cua cac bieu thc sau:

a)

b)

c) Bai 7. Giai cac he phng trnh sau:

a)

b)

c)

d)

e)

f)

g)

h)

i)

Bai 8. Giai cac he phng trnh sau:

a)

b)

c)

d)

e)

f)

g)

h)

VAN E 3: Tap hp iem

Gia s so phc z = x + yi c bieu dien iem M(x; y). Tm tap hp cac iem M la tm he thc gia x va y.Bai 1. Xac nh tap hp cac iem M trong mat phang phc bieu dien cac so z thoa man moi ieu kien sau:

a)

b)

c)

d)

e)

f)

g)

h)

i)

k)

l)

m)

Bai 2. Xac nh tap hp cac iem M trong mat phang phc bieu dien cac so z thoa man moi ieu kien sau:

a) la so thc

b) la so thuan aoc)

VAN E 4: Dang lng giac cua so phc

S dung cac phep toan so phc dang lng giac.Bai 1. Tm mot acgumen cua moi so phc sau:

a)

b) 4 4i

c)

d)

e)

f)

Bai 2. Thc hien cac phep tnh sau:

a)

b)

c)

d)

e)

f)

g)

h)

i)

k)

Bai 3. Viet di dang lng giac cac so phc sau:

a)

b)

c)

d)

e)

f)

g)

h)

i)

k)

l)

m)

Bai 4. Viet di dang ai so cac so phc sau:

a)

b)

c)

d)

e)

f)

g)

h)

i)

k)

l)

m)

Bai 5. Tnh:

a)

b)

c)

d)

e)

f)

g)

h)

i)

k)

l)

Bai 6. Chng minh:

a)

b)

c)

d)

Bai 1. Thc hien cac phep tnh sau:

a)

b)

c)

d)

e) f)

g)

h)

i)

k)

Bai 2. Cho cac so phc . Tnh:

a)

b)

c)

d)

e)

f)

Bai 3. Rut gon cac bieu thc sau:

a)

b)

Bai 4. Tm cac so thc x, y sao cho:

a)

b)

c)

Bai 5. Tm cac can bac hai cua cac so phc sau:

a)

b)

c)

d)

e)

f)

g)

h) i, i

i)

k)

l)

m)

Bai 6. Tm cac can bac ba cua cac so phc sau:

a)

b) 27

c)

d)

Bai 7. Tm cac can bac bon cua cac so phc sau:

a)

b)

c)

d)

Bai 8. Giai cac phng trnh sau:

a)

b)

c)

d)

e)

f)

g)

Bai 9. Goi la hai can bac hai cua va la hai can bac hai cua . Tnh

EMBED Equation.DSMT4 ?Bai 10. Giai cac phng trnh sau tren tap so phc:

a)

b)

c)

d)

e)

f)

g)

h)

i)

k)

l)

m)

n)

o)

p)

Bai 11. Giai cac phng trnh sau tren tap so phc:

a)

b)

c)

d)

e)

f)

g)

h)

i)

k)

Bai 12. Giai cac phng trnh sau tren tap so phc:

a)

b)

c)

d)

e)

Bai 13. Giai cac phng trnh sau biet chung co mot nghiem thuan ao:

a)

b)

Bai 14. Tm m e phng trnh sau:

a) Ch co ung 1 nghiem phc

b) Ch co ung 1 nghiem thc

c) Co ba nghiem phcBai 15. Tm m e phng trnh sau: co t nhat mot nghiem thcBai 16. Tm tat ca cac so phc z sao cho la so thc.Bai 17. Giai cac phng trnh trung phng:

a)

b)

c)

Bai 18. Cho la hai nghiem cua phng trnh: . Tnh gia tr cua cac bieu thc sau:

a)

b)

c)

d)

e)

f)

Bai 19. Cho la hai nghiem cua phng trnh: . Tnh gia tr cua cac bieu thc sau:

a)

b)

c)

Bai 20. Tm tap hp cac iem trong mat phang phc bieu dien cac so phc thoa man he thc sau:

a)

b)

c)

Bai 21. Hay tnh tong biet rang .Bai 22. Viet di dang lng giac cac so phc sau:

a)

b)

c)

d)

e)

f)

g)

Bai 23. Tm moun va mot acgumen cua cac so phc sau:

a)

b)

c)

d)

e)

f)

g)

h)

i) Bai 24. Tm moun va mot acgumen cua cac so phc sau:

a)

b)

c)

Bai 25. Chng minh cac bieu thc sau co gia tr thc:

a)

b)

c)

d)

e)

Bai 26. Trong cac so phc z thoa man ieu kien . Tm so phc z co moun nho nhat.Bai 27. Xet cac iem A, B, C trong mat phang phc theo th t bieu dien cac so phc sau:

a)Chng minh ABC la tam giac vuong can.

b) Tm so phc bieu dien bi iem D sao cho t giac ABCD la hnh vuong.Bai 28. Giai cac phng trnh sau, biet chung co mot nghiem thuan ao:

a)

b)

c)

Bai 29. Cho a thc .

a)Tnh

b) Giai phng trnh .

Bai 30. Giai phng trnh , biet la mot nghiem cua phng trnh.Bai 31. Giai cac phng trnh sau:

a)

b)

c)

d)

e)

Bai 32. Giai cac phng trnh sau:

a)

b)

c)

d)

Bai 33. Chng minh rang: neu th .

Bai 34. Cho cac so phc . Chng minh:

a)

b)

c)

d) Neu th .

Chan thanh cam n cac ban ong nghiep va cac em hoc sinh a oc tap tai lieu nay.

transitung_tv@yahoo.com

II. ON TAP SO PHC

CHNG IV

SO PHC

I. SO PHC

Trang 110Trang 111

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