Question

已知|z|=1,a属于复数,求|（z-a）/（a＊z共轭-1）|

Answer 1

用z'代表复数z的共轭复数

则：z=a+bi z'=a-bi z*z'=a^2+b^2=1

|（z-a）/（a*z'-1）|

= |z（z-a）/（z*a*z' - z）| ……上下乘以z

= | z(z-a) / (a-z) |

= | -z |

= 1