giai tich 12 - chuong iv.doc
TRANSCRIPT
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.
II. ON TAP SO PHC
CHNG IV
SO PHC
I. SO PHC
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