Given that |z1+z2|^2=|z1|^2+|z2|^2, prov...

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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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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