复数Z满足(Z-1)/(Z-2)为纯虚数,求复数在复平面上对应的轨迹方程

问题描述:

复数Z满足(Z-1)/(Z-2)为纯虚数,求复数在复平面上对应的轨迹方程

设:Z = a + bi
另设:(Z-1)/(Z-2) = ci(c不等于0)
代入计算:(a-1) + bi = (a-2)ci - bc
则有:
(a - 1) / c = -b
(a - 2) c = b
相乘:(a-1)(a-2) = -b平方
剩下的你自己化简吧