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Question 230012
JEE Mathematics · Medium

Complex Numbers: Locus MCQ

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LocusMediumQuestion 230012

Question

If |z − 1| = |z + 1|, then z lies on:
  1. A
    Imaginary axis
    Correct
  2. B
    Real axis
  3. C
    Circle |z|=1
  4. D
    Line y = x

Correct answer

Imaginary axis

Explanation

|z−1| = |z+1| means z is equidistant from 1 and −1 on the real axis. The locus is the perpendicular bisector of the segment joining 1 and −1, which is the imaginary axis (x = 0).

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