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ExamsJEE MainMaths

How many complex numbers z satisfy the condition |z - 1| = |z + 1| = |z - i|?

  1. 1
  2. 2
  3. Infinitely many
  4. 0

Correct answer: 1

Solution

The condition |z - 1| = |z + 1| describes the perpendicular bisector of the segment connecting the points 1 and -1 on the complex plane, which is the vertical line x = 0. The condition |z - i| = |z + 1| describes the perpendicular bisector of the segment connecting -1 and i, which intersects the first line at a single point, resulting in exactly one complex number that satisfies all three conditions.

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