复数的一道题求满足 |（Z+1）/(Z-1)|=1且Z+(2/Z) ∈R的复数Z
问题描述：
复数的一道题
求满足 |（Z+1）/(Z-1)|=1且Z+(2/Z) ∈R的复数Z
答
设Z=x+yi,(x,y∈R),则Z+2/Z=x+yi+2/(x+yi)=x+2x/(x²+y²)+[y-2y/(x²+y²)]i由Z+(2/Z) ∈R得y-2y/(x²+y²)=0.所以y=0或x²+y²=2若y=0,则z=x.|(Z+1)/(Z-1)|=|(x+1)/(x-1)|=1,得x=...