复数z满足|z|=2根号10,argz(z-4)=π/4

问题描述:

复数z满足|z|=2根号10,argz(z-4)=π/4

设Z=a+bi argz(z-4)=π/4
a-4=b
|z|=2根号10
a^2+b^2=40
a^2+(a-4)^2=40
2a^2-8a-24=0
a^2-4a-12=0
a=-2或a=6
a=-2 b=6 设
a=6 b=2
Z=6+2i