Question

已知为纯虚数，且(z+1)(+1)=|z|²，求复数z.

Answer 1

思路解析:先将为纯虚数的条件化简,再设z=a+bi来求解.

解:由(z+1)(+1)=|z|²z+=-1,                                              ①

由为纯虚数，+=0z·-1=0.                                ②

设z=a+bi,代入①②,得a=，a²+b²=1.

∴a=，b=.∴z=.