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NDA 2022 Maths · Mathematics · Complex Numbers and Quadratic Equations · easy

The locus of the point z in the Argand plane satisfying |z-3|=|z+3| is

Single correct option

The locus of the point zz in the Argand plane satisfying ∣z−3∣=∣z+3∣|z-3|=|z+3| is
  1. A. the real axis
  2. B. the circle ∣z∣=3|z|=3
  3. C. the imaginary axis
  4. D. the line x=3x=3
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Answer: (C) the imaginary axis

∣z−3∣=∣z+3∣|z-3|=|z+3| says zz is equidistant from 33 and −3-3, so it lies on the perpendicular bisector of the segment joining them, which is the imaginary axis (x=0x=0). Squaring gives −6x=6x-6x=6x, so x=0x=0.
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Original question written in the NDA 2022 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