2|z-2|=|z-1|not}

Write any two complex numbers,then show that |z1+z2|^2+|z1-z2|^2=2(|z1|^2+|z2|^2)

Prove that |z_1+z_2|^2 = |z_1|^2 + |z_2|^2 if z_1/z_2 is purely imaginary.

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

Given that |z_1+z_2|^2=|z_1|^2+|z_2|^2 , prove that z_1/z_2 is purely imaginary.

Prove that |z_1+z_2|^2=|z_1|^2+|z_2|^2, ifz_1//z_2 is purely imaginary.

Prove that |z_1+z_2|^2=|z_1|^2+|z_2|^2, ifz_1//z_2 is purely imaginary.

Prove that |z_1+z_2|^2=|z_1|^2+|z_2|^2, ifz_1//z_2 is purely imaginary.

If z_1, z_2 in C , then say which are true and false - . |z_1+z_2|^2=|z_1""|^2+|z_2|^2-2R e(z_1 z_2) |z_1-z_2|^2=|z_1""|^2-|z_2|^2-2R e(z_1 z_2) |z_1+z_2|^2+|z_1-z_2|^2=2(|z_1|^2+|z_2|^2) |a z_1-b z_2|^2+|b z_1+a z_2|^2=(a^2+b^2)(|z_1|^2+|z_2|^2) , where a ,b in Rdot