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NDA 2024 Maths · Mathematics · Complex Numbers and Quadratic Equations · easy

If z is a complex number satisfying |z-1|=|z+1|, then the locus of z is

Single correct option

If zz is a complex number satisfying ∣z−1∣=∣z+1∣|z-1|=|z+1|, then the locus of zz is
  1. A. the real axis
  2. B. the circle ∣z∣=1|z|=1
  3. C. the line y=1y=1
  4. D. the imaginary axis
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Answer: (D) the imaginary axis

∣z−1∣=∣z+1∣|z-1|=|z+1| says zz is equidistant from 11 and −1-1, so it lies on the perpendicular bisector of the segment joining them. That is the line x=0x=0, the imaginary axis. Trap: the real axis contains the two points but is not equidistant.
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Original question written in the NDA 2024 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake