Question

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

Answer 1

设 z=a+bi

∴√(a²+b²)=1+3i-a-bi=(1-a)+(3-b)i

∴a²+b²=(1-a)²

3-b=0

∴a=-4

b=3

∴2z/(1+i)²(3+4i)²

=2(-4+3i)/2i(24i-7)

=(-4+3i)/(-24-7i)

=(4-3i)(24-7i)/625

=(96-21-100i)/625

=(3-4i)/25