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If z1 and z2 are complex numbers with z2 != 0 satisfying |z1 + z2|² = |z1|² + |z2|², then z1/z2 is:

1. zero or purely imaginary
2. purely imaginary
3. purely real
4. none of these

Correct answer: zero or purely imaginary

Solution

The given equality removes the cross term, so z1 and z2 are perpendicular as vectors, meaning z1/z2 has zero real part (or z1 = 0).

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