If for complex numbers `z_1` and `z_2` and `|1-bar(z_1)z_2|^2-|z_1-z_2|^2=k(1-|z_1|^2)(1-|z_2|^2)` then `k` is equal to:

If for complex numbers z_(1) and z_(2) and |1-bar(z_(1))z_(2)|^(2)-|z_(1)-z_(2)|^(2)=k(1-|z_(1)|^(2))(1-|z_(2)|^(2)) then k is equal to:

Find the value of 'k' if for the complex numbers z_(1) and z_(2) . |1-bar(z_(1))z_(2)|^(2)-|z_(1)-z_(2)|^(2)=k(1-|z_(1)|^(2))(1-|z_(2)|^(2)) .

For two unimodular complex numbers z_1 and z_2, then [(bar z_1,-z_2),(bar z_2,z_1)]^-1[(z_1,z_2),(bar (-z_2),bar z_1)]^-1 is equal to

Prove that for nonzero complex numbers |z_1+z_2| |frac(z_1)(|z_1|)+frac(z_2)(|z_2|)|le2(|z_1|+|z_2|) .

If z_1ne-z_2 and |z_1+z_2|=|1/z_1 + 1/z_2| then :

If P and Q are represented by the complex numbers z_1 and z_2 such that |(1)/(z_2) + (1)/(z_1)|= |(1)/(z_2) - (1)/(z_1)| , then the circumstance of Delta OPQ (where O is the origin) is

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