if `|z_1+z_2|=|z_1|+|z_2|,` then prove that `a r g(z_1)=a r g(z_2)` if `|z_1-z_2|=|z_1|+|z_2|,` then prove that `a r g(z_1)=a r g(z_2)=pi`

If |z_1+z_2| = |z_1-z_2| , prove that amp z_1 - amp z_2 = pi/2 .

Prove that |1-barz_1z_2|^2-|z_1-z_2|^2=(1-|z_1|^2)(1-|z_2|^2) .

Prove that |(z_1, z_2)/(1-barz_1z_2)|lt1 if |z_1|lt1,|z_2|lt1

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

If |z_1|=1,|z_2|=1 then prove that |z_1+z_2|^2+|z_1-z_2|^2 =4.

Prove that |z_1+z_2|^2+|z_1-z_2|^2 =2|z_1|^2+2|z_2|^2 .

If |z_(1)+z_(2)|>|z_(1)-z_(2) then prove that -(pi)/(2)

If z_(1)=iz_(2) and z_(1)-z_(3)=i(z_(3)-z_(2)), then prove that |z_(3)|=sqrt(2)|z_(1)|

Statement I: If |z_1+z_2|=|z_1|+|z_2|, then Im(z_1/z_2)=0 (z_1,z_2 !=0) Statement II: If |z_1+z_2|=|z_1|+|z_2| then origin, z_1, z_2 are collinear with 'z_1' and z_2 lies on the same side of the origin (z_1,z_2 !=0)