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Prove that |z1+z2|^2=|z1|^2+|z2|^2, ifz1...

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

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

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