内容正文:
书书书
!
b=2,
"#
z=2+2i,
"#
z·珋z=|z|2 =8.
!
、
"#$
9.1+i; 10.1+2i;
%&
:
9.i+i3+i5+i8 =i-i+i+1=1+i.
10.
$
z=a+bi(a,b∈R),%&2(a+bi)-(a-bi)
=1+6i,
'(!
a+3bi=1+6i,
)!
a=1,
b=2{ ,"#z=
1+2i.
'
、
()$
11.
(
:
$
z=a+bi(a,b∈R),%&
a2-b2+2abi=12-16i,
"#
a2-b2 =12,
2ab=-16{ , )!
a=-4,
b=2{ , *
a=4,
b=-2{ .
"#
z=-4+2i
*
z=4-2i.
12.
(
:
$
z=a+bi,a,b∈R,
+,
|z|=1+3i-z,
"#
a2+b槡
2 -1-3i+a+bi=0.
%
a2+b槡
2 +a-1=0,
b-3=0{ , )!
a=-4,
b=3{ .
-
z=-4+3i.
"#
(1+i)2(3+4i)2
2z =
2i(-7+24i)
2(-4+3i)
=24+7i4-3i=3+4i.
13.
(
:
+,
z=1+i,
"#
z2 =2i.
"#
z2+az+b
z2-z+1
=2i+a+ai+b2i-1-i+1 =
(a+2)i+(a+b)
i =a+2-(a+b)i=1-i.
"#
a+2=1,
a+b=1{ ,
)!
a=-1,b=2.
14.
(
:
./0!
z1 =
-1+5i
1+i =2+3i,
12
|z1-珋z2|=|4-a+2i|= (4-a)
2+槡 4,
|z1|=槡13.
+,
|z1-珋z2|<|z1|,
"#
(4-a)2+槡 4<槡13,
3
a2-8a+7<0,
)!
1<a<7.
*
34
+
3
,-.)/
012345602789:;<$
=
、
>?$
1~6 ACBBBB 7~12 BDDBCC
%&
:
1.1-i
1+( )i
2 [= (1-i)2(1+i)(1-i ])
2
=(-i)2=-1,
-4
(A).
2.
5 6 7 8 9 : ; < =
z = 2-3i1+i =
(2-3i)(1-i)
2 =-
1
2-
5
2i,3z>7?@A9BC,
-12,-( )52 ,"#>DEFG.
3.
+,
(1+ai)2-2i=1-a2+2ai-2i=(1-a2)
+(2a-2)i,
./0<!
1-a2 =0,
2a-2≠0{ ,)! a=-1.-
(B)
HI
.
4.z= 2ii-1+i
3= -2i(1+i)
(1-i)(1+i)-i=-(i-1)-
i=1-2i,
JKL78,
1+2i.
6.
MNO78P,Q8
,
%<#RSTU
,
-
(A)
V
W
.
M78
z
,Q8
,
%JXY,
0,z=z;
M78
z=z,
%
JXY,
0,z
,Q8
,
"#78
z
,Q89Z[\]2
z
=z,(B)
HI
.
78
z
9QY,
0,ẑ
_`2aX8
,(C)
VW
.
78
i+1
9KL782
1-i,(D)
VW
.
7.
./0!
,z= 5i-2=
5(-i-2)
(i-2)(-i-2)=-2-i,
"#
z=-2+i,
"#78
z
bc9de1DfFG
.
8.
gh
→OA
bc9d,
(5,3),
+,
→OB
i
→OA
j1X
kbl
,
"#
→OB
bc9d,
(-5,3),→OB
bc978,
-5+3i.
9.
./0!
,
1-槡3z
1+槡3z
=iz= 1-i
槡3(1+i)
=-槡33i,"
#
|z|=槡33.
10.
.槡2cosθ+1=0!θ=2kπ±
3π
4.
mθ=2kπ+3π4n,2θ=4kπ+
3π
2,
sin2θ-1=-2,op/0;
mθ=2kπ-3π4n,2θ=4kπ-
3π
2,
sin2θ-1=0,̂ op/0,qr.
11.z=1+ 2i1-i=1+
2i(1+i)
2 =i,
"#
1+z+z2 +… +z2014 =1×(1-z
2015)
1-z =
1-i2015
1-i =
1-i4×503+3
1-i =
1+i
1-i=
(1+i)2
(1-i)(1+i)=
2i
2 =
i.
12.
st^uvwxy9?@z{
,
.78|}9~
�0�<=
|z-1+2i|=|z-(1-2i)|,
Jxy7?@
A
,
<�{��0_d
Z(x,y)
�d
A(1,-2)
9��
,
8
��p<=
,ZA
9�U�,d
A(1,-2)
���
x+y=
0
9��
,
��d���9���v;!��,
槡2
2.
!
、
"#$
13.0; 14.槡2; 15.-i;