ÔN TẬP SỐ PHỨC

{ }

    z z a bi a b i= = + ∈ = −C R
 !"#
•  
⇔
$
≠
$
• %"#
⇔
$
≠
$
&'(
biaz −=
−
)*+,%(
 
z a b= +
-./0%1 /0%!"#/0%
234534
6R∈
,78%9:;,8<*5346
=>?0!@A B7,
CDE BF#G%4HE,@I4

J
@#0KLG%",7

M>Nhân tử và mẫu với số phức liên hợp của mẫu
$>N( E<
| |.a i±
17O0@

$5∈PQ$6


)b ac∆ = −
6
$=∆
17O0@R0B<9%4S

b
a
−
6
$∆ >
17O0@R0B< EB


b
z
a
− ± ∆
=
6
$∆ <
17O0@R0B<EB



b i
z
a
− ± ∆
=
BÀI TẬP:
T>#U
 &z i= +
!
 w i= −
<<+,%!'(U!V
W
 &  )
  z z w w

X

  &z i= − +

&
Cz = −

 )
    = ) w i w i= − − = − +

T BUYW
65Z&6

Z565-Z6 6

( )
) 
- 
&
i
i
i
+
− + −
−

6
6655
&
ii
i
+−
+
96


656&5
6565
ii
ii
+−+
−−+
F6
- $
5 & 6 5 6i i− +

[6
( )
( )

M
 &

i
i
+
−
06
C
- =
2
i
i
+
 
 ÷
+
 
ĐS:
$ =i
− −

2 i
− +

i

-
&
-
)
+
9
i
=
M
&)

+

F
$
 i
−
[
2
  & 5 &6i
 
− − + +
 
0
M
 i
T&<L
6
 & = Cz i i+ = +
6

( ) ( )
 & ) & = -i z i i− + + = −
6
( )
 &  )i z i z+ + = −
96
( )
  - 2
 &
z
i i
i
− + = −
+
F6
z

$
!"#(/0& (R
[6
z

&)
!
2z z
−
+ =
06
z =
! /0"#

T)\"U7O0@%@'>5]6
6
i
i
z
i
i
+
+−
=
−
+

&


X
i
-
)
-

+

6
$6


^5&6_5 =+++−
i

izizi
XJ
6
izz ) −=+
X&) 
96
$

=− zz
X$J
ii

&




&


−+
F6
$

=+ zz
X$J 
[6

& )z i= − +
XJJ

T-`U,aU,8<@#0<bc08%9:U
d<e<f,g%KB
6
)& =++ zz
6
izz −+− 
6
5  6 $z i+ − =
X63!3J=64

&±
6
 
5 6 5 6 $x y+ + − =
T=\"U7O0@%@#0>
6

&  $x x+ + =
b)

 $x x+ + =
6
$&

=+− xx
96
&
C $x − =

X6

 &
2
i− ±
6
 &

i− ±
6
i



&
±
96
  &i− ±
TC\"U7O0@%@#0>

ÔN TẬP SỐ PHỨC
6
) 
& ) $z z+ − =
5X
 i± ±
6 6
) 
C M $z z− − =
5X
 &i± ±
6

TM\"U7O0@%@#0>
6
( )
( )

 &  $z i z z+ − − + =
6
&
 $z + =

XJ&
 &
 
i±
J
 &
 
i− ±
T$>#7O0@
&
 $z − =
RU0B<




&
\hiT>7U,8<8%9:U





&
>0<
ABC∆
<0U,g%
T. `YU,8<iT>@#0<bc0j34F# 8%9:U

  &
)  2
 5 65  6
 &
z
i i
i i
i i
= = =
+
− +
− −

6>0<iT><0U!%+0E
6<8%9:;,8<k##0UiT>k!%+0
CÁC ĐỀ THI VỀ SỐ PHỨC
1) < "#!<+,%(<f%
56

5Z6C565>XZ$$M6
2) Giải các phương trình sau trên tập số phức:
6C


Z)$5>TlD$$M66
4 3 7
2
z i
z i
z i
− −
= −
−
5>X$M6
6

Z$5D>lD$$M6
96

$$5

!

0B<6
W0U@a8%
2 2
1 2
A z z= +
5X.miZ$$M6
3)>#
 
    &z i z i= + = −
5D$$T>T6

`U,a !"#(
 
z z−

4)>#
 
 -  & )= + = −z i z i
5D$$TD>6
`U,a !"#(
 
z z

5) \"15Z65J6)J-5D$6
6)>#d<e

5  6 ) $i z z i+ + = −
Wnn5>X$6
7)<d<enn

!

%"#
8)`U,aU,8<8%9:d<e<f,g%KB
nJ5&J)6n5>X$$M6
9)<S"UL

nn


z

5X.k.mil$6
10)<L
- &
 $
i
z
z
+
− − =
5X.mTl$6
11)i$>#d
( )
3
1 3.i
z
1 i
-
=
-
<
z iz+
12)k<d
( )
z 2 3i .z 1 9i- + = -
13)\h

!

0B<(


$$W
2 2 4 4
1 2 1 2
z z ; z z+ +
X$$$
14)>#

!

d
1 2 1 2
z z 1; z z 3= = + =
W
1 2
z z-
X
15)>#

!

d
1 2 1 2
z 3; z 4; z z 37= = - =
<
1
2
z
z

16)T<L

5 i 3
z 1 0
z
+
- - =

17)T< !"#L
21
1 i 3
z
1 i
æ ö
+
÷
ç
÷
=
ç
÷
ç
÷
÷
ç
+
è ø

18)k>#d<e
( )
( )
  

 = C

i
i Z i
i
+
+ + = +
+
<<+,%(

w z i= + +
19)i>#d
( )
-


z i
i
z
+
= −
+
W
w
!o

w z z= + +

20) >X>#d
( )

2
z 2 1 i .z 2i 0- + + =
< !"#(
1
z

21)<34
R∈
d
( )
( )
   
 & ) x y x y i xy xy i+ + + = + + +

22)<U0%4'34##34d
2
z 4 6 5i= +

<U0%4'34##34d
3
z 18 26i= +

X3
±
&4
-±
b/ 3&4
24)k$pL9q0700UU0B<(7O0@

 & ) $z iz− − =

25)>kk$\h
 
z z,
U0B<(

   $z z i− + + =
W
 
z z+

26)`U,aU,8<@#0<8%9:(d

z
z i
=
−

27)>#d
( ) ( )

  &

i
i z i z
i
−
− − = −
+
<h,?,8<8%9:(
@#0j34

