f(z+i)=1-z的共轭复数,z1=1+i,z2=1-i,则f(1/z1+1/z2)=请详述

Question

f(z+i)=1-z的共轭复数,z1=1+i,z2=1-i,则f(1/z1+1/z2)=
请详述

Answer 1

令z=a+bi
f(z+i)=1-z f[a+(b+1)i]=1-(a-bi)=-a+(b+1)i
1/z1+1/z2=1/(1+i)+1/(1-i)=(1-i)/2 +(1+i)/2=1
f(1)=-1