Question

若复数Z满足（Z-1）/（Z+1)为纯虚数,求Z在复平面上对应点的轨迹方程

Answer 1

z=x+yi

则(z-1)/(z+1)

=[(x-1)+yi][(x+1)-yi]/[(x+1)-yi][(x+1)+yi]

=[(x²-1+y²)+2yi]/(x²-2x+1+y²)

纯虚数则x²-1+y²=0,2y≠0

所以x²+y²=1,不包括(±1,0)