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)