Question

已知复数z满足：|z|=1+3i-z，求

(1+i)2(3+4i)2

2z

的值．

Answer 1

设z=a+bi，（a，b∈R），而|z|=1+3i-z，
即

a2+b2

-1-3i+a+bi=0
则 

a2+b2 +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