Let `z_1, z_2` be two complex numbers with `|z_1| = |z_2|`. Prove that `((z_1 + z_2)^2)/(z_1 z_2)` is real.

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

Let z_(1),z_(2) be complex numbers with |z_(1)|=|z_(2)|=1 prove that |z_(1)+1|+|z_(2)+1|+|z_(1)z_(2)+1|<=2

If z_1 and z_2 are two distinct non-zero complex number such that |z_1|= |z_2| , then (z_1+ z_2)/(z_1 - z_2) is always

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

Let z_(1),z_(2) be two complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| . Then,

Let z_1 , z_2 be two complex numbers such that (z_1-2z_2)/(2-z_1barz_2) is unimodular . If z_2 is not unimodular then find |z_1| .

For any two complex number z_(1) and z_(2) prove that: |z_(1)+z_(2)|>=|z_(1)|-|z_(2)|