Chinh phục chuyên đề số phức Thầy Hiếu live

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CHINH PHụC

CHUYÊN Đề:
S PH C
tHầY HIếU LIVE
HọC VIÊN:
TÔI QUYếT TÂM THI ĐậU ĐạI HọC

Toán
học

Khóa học Luyện Thi Đại Học – Thầy Hiếu Live – 0988 593 390 – Facebook: Hiếu Live

MỤC LỤC GIÁO ÁN SỐ PHỨC
STT

BUỔI

Kiến thức

Trang

1.

Kiến thức cơ bản về số phức

2

2.

Dạng 1: Các lý thuyết cơ bản về số phức

3

3.

Bài toán 1: Công trừ số phức

3

4.

Bài toán 2: Nhân hai số phức

3

Bài toán 3: Môđun số phức

3

6.

Bài toán 4: Số phức liên hợp

4

7.

Bài toán 5: Chia hai số phức

5

5.

BUỔI 1

Dạng 2: Tìm số phức z thỏa mãn phương trình

8.

8

Bài toán 1: Tìm số phức z thỏa mãn PT chỉ chứa z hoặc z

8

Bài toán 2: Tìm số phức z thỏa mãn PT chứa z; z; z

11

Bài toán 3: Tìm số phức z thỏa mãn 2 điều kiện PT

19

12.

Bài toán 4: Số thuần ảo, số thực

22

13.

Bài toán 5: Biến đổi mũ to

27

9.
10.
11.

14.

BUỔI 2

BUỔI 3

Dạng 3: Giải phương trình số phức

30

Căn bậc hai số phức

30

16.

Bài toán 1: Detal âm và dương

33

17.

Bài toán 2: Detal là số phức

37

18.

Bài toán 3: Phương trình bậc cao

40

Bài toán 4: Phương trình biết nghiệm

42

15.

19.
20.

BUỔI 4

Dạng 4:Tập hợp điểm biểu diễn số phức

43

21.

Bài toán 1: Tìm điểm biểu diễn số phức z

43

22.

Bài toán 2: Tập hợp điểm biểu diễn số phức z

45

Bài toán 3: Biểu diễn số phức w thông qua z

47

23.
24.

BUỔI 5

25.
26.

BUỔI 6

Dạng 5:Tìm số phức thỏa mãn môđun nhỏ nhất

48

Đáp án

52

TỔNG ÔN THI THỬ CUỐI CHUYÊN ĐỀ
Lì xì giải nhất – nhì – ba – khuyến khích

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BÀI TẬP VỀ NHÀ CÁC BUỔI
BUỔI

BÀI TẬP

BUỔI 1

FINISH

BUỔI

BÀI TẬP

H1 – H20

BUỔI 4

H107 – H130

BUỔI 2

H21 – H62

BUỔI 5

H131 – H142

BUỔI 3

H63 – H106

FINISH

LÌ XÌ CHĂM CHỈ CÁC BUỔI
BUỔI

LÌ XÌ CHĂM CHỈ

BUỔI 2

10.000

BUỔI 4

10.000

BUỔI 6

10.000

XÁC NHẬN GIÁO VIÊN

LÌ XÌ THI CUỐI CHUYÊN ĐỀ

QUYẾT TÂM ĐẬU ĐẠI HỌC EM NHÉ!
NOTHING IS IMPOSSIBLE 

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DẠNG 1: CÁC LÝ THUYẾT CƠ BẢN VỀ SỐ PHỨC
BÀI TOÁN 1: Cộng trừ số phức: Cho z1  a1  b1i; z 2  a 2  b 2 i

k.z1  k.a1  k.b1i;

z1  z 2   a1  a 2    b1  b 2  i;

z1  z 2   a1  a 2    b1  b 2  i

Một hành trình ngàn dặm luôn bắt đầu bằng một bước đơn giản đầu tiên.
TN 2010 (CB) Cho hai số phức z1  1  2i; z 2  2  3i .
a)

H1.

Xác định phần thực và phần ảo của số phức z1  2z 2

Đáp án: 3  8i

b) Xác định phần thực và phần ảo của số phức 3z1  2z 2

Đáp án: 1  12i

c) Xác định phần thực và phần ảo của số phức z1  2z 2

Đáp án: 5  4i

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Môđun số phức z là độ dài đoạn OM với M(a;b)
Cho hai số phức z1  1  i; z 2  3  2i
a) Tính môđun của số phức z1 ; z 2

Đáp án: z1  2; z 2  13

b) Tính mô đun của số phức z1  z 2 ; z1  z 2 ; z1  2z 2
H3.

Đáp án: z1  z 2  5; z1  z 2  5; z1  2z 2  74
c) Tính mô đun của số phức z1.z 2 ; z1 (z1  z 2 ); z 2 (z1  2z 2 )
Đáp án: z1.z 2  26; z1 (z1  z 2 )  5 2; z 2 (z1  2z 2 )  442

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Đáp án: z  34  22i

c) Tìm số phức liên hợp của số phức  z1  1 (2i  z 2 )

Đáp án: z  39  3i

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BÀI TOÁN 5: Chia hai số phức Cho z1  a1  b1i; z 2  a 2  b2i

z1 z1.z 2 (a1  b1i)(a 2  b 2i) (a1  b1i)(a 2  b 2i)



z 2 z 2 .z 2 (a 2  b 2i)(a 2  b 2i)
a 22  b22

H6.

TN 2012 Tìm các số phức

25i
; biết z  3  4i
z

Đáp án: 4  3i

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H7.

Tìm số phức z biết z 

1  9i
 5i
1 i

Đáp án: 4

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Tìm số phức z biết:
a)z 

3  4i
2i

 2  3i 
b)z 

Đáp án: z 
2

3  4i

H8.

2 11
 i
5 5

c)z   3  4i  

5  7i
6  5i

Đáp án: z  

63 16
 i
25 25

Đáp án: z  

188 177

i
61 61

d)z 

8  5i 2i  1

3  4i 3  2i

Đáp án: z 

27 411

i
325 325

e)z 

1
2  3i

Đáp án: z 

2 3
 i
13 13

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BÀI TẬP TỔNG HỢP DẠNG I:

Có trải qua đau khổ, cay đắng con người ta mới hiểu ra được nhiều điều, mới
nhìn nhận ra được những sự thật mà nếu như ta sống một cuộc sống êm đềm và
hạnh phúc ta không thể nhận ra.
Hãy viết các biểu thức sau dưới dạng số phức z = a + bi (a,b  R)

A  (3i  4)  (3  2i)  (4  7i)

Đáp án: A  55  15i

B   7  5i 1  i    3i  2 

Đáp án: B  10  i

2

C   3  4i   5  7i 
3

2

3

2

D   3  i   1  2i 

H9.

Đáp án: C  133  169i

E   3  i   3  2i 
G  1  4i  (1  i)3
H  (1  2i)(3  i) 

Đáp án: D  21  30i
Đáp án: E  222  346i

Đáp án: G  1  2i

2(2  3i)
 4  2i
1 i

1  i 3  i 1  2i


1 i 2  i 1 i
1
K  (1  i)(3  2i) 
3 i
I

Đáp án: H  4  2i
1 7
 i
10 10
53 9
Đáp án: K 
 i
10 10

Đáp án: I  

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Tìm phần thực ; phần ảo và số phức liên hợp, môđun của mỗi số phức sau:
z1  (2i  1)2  3i(i  1)  2i 3

z2 

H10.

3  2i
 3i
i2

Đáp án: z  9i; z  9i; z  9
Đáp án: z 

4 22
4 22
 i; z   i; z  2 5
5 5
5 5

z 3  (2  3i) 2  (1  i)2

Đáp án: z  5  10i; z  5  10i; z  5 5

z 4  (3  2i)3

Đáp án: z  9  46i; z  9  46i; z  2197

z 5  (2i  1)2  (3  i)2

Đáp án: z  11  10i; z  11  10i; z  221

z 6  (3  4i)(2  i)  5  7i

Đáp án: z  3  4i; z  3  4i; z  5

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9 13
 i
10 10

b) (3  i)z  5  7i  0

Đáp án: z 

11 8
 i
5 5

c) ( 3  i)z  4  (5  3i)( 4  5i)

Đáp án:

d) (5  3i)z  (1  i)2

Đáp án: z  

e) (2  3i)2 z  (1  3i) 2  0
f)

z  2  3i
 4  2i
zi

52 39
 i

5
5

3 5
 i
17 17
32 126
Đáp án: z  

i
169 169

Đáp án: z 

2 29
 i
13 13

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H14.

A-2010. Tìm phần ảo của số phức z biết z 



2

 

2  i . 1  2.i



Đáp án: b   2

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số phức w  (1  z)z .
Đáp án: a  3; b  1

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H19.

Tìm môđun của số phức z 

(1  i)(2  i)
.
1  2i

Đáp án: z  2.

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H20.

Tìm môđun của số phức: z 

1  2i  (1  i)3
1 i

Đáp án: z 

5 2
2

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BÀI TOÁN 2: Tìm số phức z thỏa mãn PT có chứa 2 trong 3 thành phần z; z; z
 Phương pháp: Gọi z = a + bi (a,b  R)
 Nếu đề có z => z = a – bi
 Nếu có z => z  a 2  b2
Áp dụng hai số phức bằng nhau: a = a’ ; b = b’
Hai trường hợp xảy ra: Lưu ý: CÔNG THỨC KIẾM HIỆP (THỰC = THỰC ; ẢO = ẢO)
-

a  a '
Khi biến đổi được a + bi = a’ + b’i 
b  b '

a  0
Nếu một bên là a + bi = 0 => 
b  0

Gieo suy nghĩ, gặt hành động. Gieo hành động, gặt thói quen. Gieo thói quen, gặt
tính cách. Gieo tính cách, gặt số phận
H21.

D - 2011.Tìm z thỏa z   2  3i  .z  1  9i

Đáp án: z  2  i

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A – 2011 NC Tính môđun của số phức z, biết: (2z  1)(1  i)  (z  1)(1  i)  2  2i
H24.
Đáp án: z 

2
3

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Cho số phức z thỏa mãn: z  2z  (1  2i) 2 (1  i) . Tìm modun của số phức z.
H25.
Đáp án: z 

442
3

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H26.

3

Tìm phần ảo của z biết: z  3z   2  i   2  i 

Đáp án: b = -10

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Xác định phần ảo z và tính môđun số phức z , biết: z  (1  9i)  (2  3i)z
H27.

Đáp án: b  1; z  5

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Đáp án: z  1  i

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H33.

Tìm mô đun của số phức z, biết rằng

z
 (4  3i)z  26  6i

2i

Đáp án: z  5

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H34.





2

Tìm phần ảo của số phức z , biết z  3z  1  2i .

Đáp án: b  2

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H35.





2

Tìm phần ảo của số phức z , biết z  1  i  z  1  2i .

Đáp án: b  3

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

5 zi
H36.

A-2012. Cho số phức z thỏa

z 1

  2  i .Tính mô đun của số phức w  1  z  z

2

.

Đáp án: w  13

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z 1

Đáp án: A  3

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H43.

Tìm số phức z thỏa mãn (z  1)(1  i) 

z 1
2
 z
1 i

Đáp án: z  i; z  

3 1
 i
10 10

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H45.

Tìm số phức z thỏa mãn điều kiện z.z  2.z  19  4i

Đáp án: z  3  2i; z  5  2i

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2

Tìm số phức z thỏa mãn (z  1)2  z  1  10i  z  3

1
Đáp án: z  1  2i; z    5i
2

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H49.

Tìm số phức z thỏa mãn: z 

25
 8  6i
z

Đáp án: z  4  3i

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Đáp án: z  3  2i; z  3  2i

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H52.

Tìm số phức z # 0, biết z.z  10(z  z) và phần ảo của z bằng ba lần phần thực của nó.
Đáp án: z  2  6i

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Đáp án: z  3  5i; z  

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Tìm số phức z thoả mãn : z  2  i  2 . Biết phần ảo nhỏ hơn phần thực 3 đơn vị.
H57.
Đáp án: z  2  2  (1  2)i; z  2  2  ( 1  2)i

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Trung Tâm Olympia – Uy Tín – Chất Lượng – Tận Tâm

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H58.

Tìm số phức z thỏa mãn z  1  5 và

1 1 5
 
z z 17

Đáp án: z  5  3i; z  5  3i

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Đáp án: z  2  6i; z 

7 21
 i
5 5

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Trung Tâm Olympia – Uy Tín – Chất Lượng – Tận Tâm

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H61.

Tìm số phức z biết rằng z  3  3i  4 2 và

z 1
1
zi

Đáp án: z  1  i; z  7  7i

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