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 the complex numbers z_1 and z_2 abs(1-barz_1z_2)^2-abs(z_1-z_2)^2 = k(1-abs(z_1)^2)(1-abs(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 any two complex numbers z_1 and z_2 prove that: |\z_1+z_2|^2 +|\z_1-z_2|^2=2[|\z_1|^2+|\z_2|^2]

If for the complex numbers z_1 and z_2 , |z_1+z_2|=|z_1-z_2| , then Arg(z_1)-Arg(z_2) is equal to

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|

For any two complex numbers z_1 and z_2 prove that: |\z_1+z_2|^2=|\z_1|^2+|\z_2|^2+2Re bar z_1 z_2

If z_1 , and z_2 be two complex numbers prove that |z_1+z_2|^2+|z_1-z_2|^2=2[|z_1|^2+|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