z是虚数,设z=a+bi,（a,b∈R,且b≠0）∴ z+1/z=1∴ a+bi+1/(a+bi)=1∴ a+bi+(a-bi)/(a²+b²)=1∴ a+a/(a²+b²)=1且b-b/(a²+b²)=0∴ a²+b²=1,∴ a=1/2∴ b=±√3/2∴ (z-1)/(z+...
已知z是虚数,且z+1/z是实数1,求z-1/z+1
z是虚数,设z=a+bi,（a,b∈R,且b≠0）∴ z+1/z=1∴ a+bi+1/(a+bi)=1∴ a+bi+(a-bi)/(a²+b²)=1∴ a+a/(a²+b²)=1且b-b/(a²+b²)=0∴ a²+b²=1,∴ a=1/2∴ b=±√3/2∴ (z-1)/(z+...