已知复数Z满足Z+1/Z∈R,且（Z-2)的模=2,求Z

题目

已知复数Z满足Z+1/Z∈R,且（Z-2)的模=2,求Z

答案

设z=x+yiz+1/z=(x+yi)+1/(x+yi)=(x+yi)+(x-yi)/(x²+y²)=x+x/(x²+y²)+[y-y/(x²+y²)]i∈R,y-y/(x²+y²)=0,得x²+y²=1|z-2|=|x+yi-2|=|(x-2)+yi|=√[(x-2)²+y&su...