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" Prove that "|z(1)+z(2)|^(2)=|z(1)|^(2)...

" Prove that "|z_(1)+z_(2)|^(2)=|z_(1)|^(2)+|z_(2)|^(2)," if "z_(1)/z_(2)" is purely imaginary."

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Prove that |z_(1)+z_(2)|^(2)=|z_(1)|^(2)+|z_(2)|^(2),quad if z_(1)/z_(2) is purely imaginary.

Prove that |z_1+ z_2|^2= |z_1|^2+ |z_2|^2 if and only if (z_1/z_2) is purely imaginary.

Prove that |z_(1) + z_(2)|^(2) + |z_(1)-z_(2)|^(2)=2|z_(1)|^(2) + 2|z_(2)|^(2)

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

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

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

For any two complex numbers z_(1) and z_(2) prove that: |z_(1)+z_(2)|^(2)=|z_(1)|^(2)+|backslash z_(2)|^(2)+2Rebar(z)_(1)z_(2)