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

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

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Given
`|z_(1)+z_(2)|^(2)=|z_(1)|^(2)+|z_(2)|^(2)`
or `|z_(1)|^(2)+|z_(2)|^(2)+z_(1)bar(z)_(2)+bar(z)_(1)z_(2)=|z_(1)|^(2)+|z_(2)|^(2)`
or `z_(1)bar(z)_(2)+bar(z)_(1)z_(2)=0`
or `(z_(1))/(z_(2))+(bar(z)_(1))/(bar(z)_(2))=0`
or `(z_(1))/(z_(2))+(bar(z)_(1))/(z_(2))=0`
Hence, `(z_(1))/(z_(2))` is purely imaginary
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