If `z_1` and `z_2` two different complex numbers and `|z_2|= 1` then prove that `|(z_2-z_1)/(1-barz_1z_2)|=1`

If z_1 and z_2 are two complex numbers such that |z_1|lt1lt|z_2| then prove that |(1-z_1barz_2)/(z_1-z_2)|lt1

If z_1 and z_2 are two complex numbers such that |z_1|lt1lt|z_2| then prove that |(1-z_1barz_2)/(z_1-z_2)|lt1

If z_1 and z_2 are two complex number such that |z_1|<1<|z_2| then prove that |(1-z_1 bar z_2)/(z_1-z_2)|<1

If z_1 and z_2 be two non-zero complex numbers such that |z_1+z_2|=|z_1|+|z_2| ,then prove that argz_1-argz_2=0 .

For two complex numbers z_(1) and z_(2) , we have |(z_(1)-z_(2))/(1-barz_(1)z_(2))|=1 , then

For two complex numbers z_(1) and z_(2) , we have |(z_(1)-z_(2))/(1-barz_(1)z_(2))|=1 , then

If z_(1) and z_(2) are two complex number such that |z_(1)|<1<|z_(2)| then prove that |(1-z_(1)bar(z)_(2))/(z_(1)-z_(2))|<1

If z_(1) and z_(2) are two complex numbers such that |z_(1)| lt 1 lt |z_(2)| , then prove that |(1- z_(1)barz_(2))//(z_(1)-z_(2))| lt 1

If z_(1) and z_(2) are two complex numbers such that |z_(1)| lt 1 lt |z_(2)| , then prove that |(1- z_(1)barz_(2))//(z_(1)-z_(2))| lt 1