已知复数z满足:|z|=1+3i-z,求 (1+i) 2 (3+4i) 2 2z 的值

已知复数z满足:|z|=1+3i-z,求 (1+i) 2 (3+4i) 2 2z 的值.
2025-06-27 01:41:20
推荐回答(1个)
回答1:

设z=a+bi,(a,b∈R),而|z|=1+3i-z,
a 2 + b 2
-1-3i+a+bi=0

则 
a 2 + b 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+7i
4-i
=3+4i