If S = z ∈ C : z - i z + 2 i ∈ R , then

If S=z∈C:z-iz+2i∈R, then
  1. S is a circle in the complex plane
  2. S contains exactly two elements
  3. S contains only one element
  4. S is a straight line in the complex plane

Solution

Given z-iz+2i∈R

Then argz-iz+2i is 0 or π

⇒S is straight line in complex plane.

Asked in: JEE Main 2021 (27 Aug Shift 1)

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