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JEE Main 202127 AugustMorning Shift
Exam
JEE Main
Year
2021
Date
27 August
Shift
Morning Shift
Subject
Mathematics
Chapter
Complex Number

JEE Main 2021 · 27 August · Morning Shift · Mathematics · Complex Number

If S = \ z ∈ C: (z - i)/(z + 2i) ∈ R\ , then

If S={z∈C:z−iz+2i∈R}S = \left\{z \in C: \dfrac{z - i}{z + 2i} \in R\right\}, then

Options

  1. ASS is a circle in the complex plane
  2. BSS contains exactly two elements
  3. CSS contains only one element
  4. DSS is a straight line in the complex plane

Correct answer

D. SS is a straight line in the complex plane

Step-by-step solution

Given z−iz+2i∈R\dfrac{z - i}{z + 2i} \in R

Thenarg(z−iz+2i)is0orπ\text{Then}arg\left(\dfrac{z - i}{z + 2i}\right)\text{is}0\text{or}\pi

⇒⇒SS is straight line in complex plane.

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