If `z_1` is a complex number other than -1 such that `|z_1|=1\ a n d\ z_2=(z_1-1)/(z_1+1)` , then show that the real parts of `z_2` is zero.

If z_(1) is a complex number other than -1 such that |z_(1)|=1 and z_(2)=(z_(1)-1)/(z_(1)+1), then show that the real parts of z_(2) is zero.

If |z + 1| = 1(z_(1) ne - 1 ) and z_(2) =(z_(1)-1)/ (z_(1)-2) , then show that the real part of z_(2) is zero.

If z_(1) and z_(2) are two complex numbers such that |z_(1)|= |z_(2)|+|z_(1)-z_(2)| then

If z_(1) and z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1, then

If z_(1) and z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 , then