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JEE Main 2019 · 12 April · Shift I

JEE Main 2019 Mathematics question on Complex Numbers and Quadratic Equations

The equation ∣z−i∣=∣z−1∣|z - i| = |z - 1|, i=−1i = \sqrt{-1}, represents
  1. A.
    a circle of radius 12\dfrac{1}{2}
  2. B.
    the line passing through the origin with slope 1
  3. C.
    a circle of radius 1
  4. D.
    the line passing through the origin with slope −1-1
Show answer and solution

Correct option: B

Solution

Let z = x + iy. Then |z - i| = |z - 1| becomes |x + i(y-1)| = |(x-1) + iy|, giving x² + (y-1)² = (x-1)² + y². Expanding: x² + y² - 2y + 1 = x² - 2x + 1 + y², which simplifies to -2y = -2x, i.e., y = x. This is a line through the origin with slope 1.

[JEE Main 2019 · 12 April · Shift I]

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