Let z₁ and z₂ be two complex numbers such that |(z₁+z₂)/(z₁−z₂)| = 1, then what is Re(z₁/z₂) + 1 equal to?
A.−1
B.0
C.1✓ Correct
D.5
Explanation
|z₁+z₂| = |z₁−z₂| implies z₁/z₂ is purely imaginary (the locus where sum and difference have equal magnitudes means perpendicularity). So Re(z₁/z₂) = 0, giving Re(z₁/z₂) + 1 = 1.
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