Question

已知Z为复数,Z≠±1,又(z-1)/(z+1)为纯虚数,求|Z|的值

Answer 1

因(z-1)/(z+1)为纯虚数

故设(z-1)/(z+1)=ki（k∈R,k≠0)

解之z=(1+ki)/(1-ki)

故|Z|=|(1+ki)/(1-ki)|

=|1+ki|/|1-ki|

=1

(1+ki与1-ki共轭)