已知复数Z=1+i求满足aZ+2bˉZ=（a+2Z)^2的实数a,b的值Z上面的ˉ

Question

已知复数Z=1+i求满足aZ+2bˉZ=（a+2Z)^2的实数a,b的值
Z上面的ˉ

Answer 1

a(1+i)+2b(1-i)=(a+2+2i)^2
a+2b+(a-2b)i=(a+2)^2-4+4(a+2)i
a+2b=(a+2)^2-4
a-2b=4(a+2)
2b= -3a-8
-2a-8=(a+2)^2-4
a^2+6a+8=0
a=-2,-4
b=-(3a+8)/2=-1,2
(a,b)= (-2,-1) or (-4,2)