JEE Main 2021 · MathsMultiple choiceSingle correctMediumConceptual

JEE Main 27 August 2021, Shift 1, Maths Q62

Question 62 of 90 in this shift, Maths question 2 of 30, Section A.

S=\left\{z \in \mathbb{C} : \frac{z-i}{z+2i} \in \mathbb{R}\right\}

, then :

(1)S contains only one element
(2)S contains exactly two elements
(3)S is a straight line in the complex planeOfficial answer
(4)S is a circle in the complex plane

Official answer

Option 3

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Complex Numbers - Polar Form
Idea tested: Collinearity via Argument

Same topic in other shifts

All Complex Numbers - Polar Form questions

2 Apr 2026, Shift 2 · Q2Let the circles $C_1: |z| = r$ and $C_2: |z - 3 - 4i| = 5, z \in \mathbb{C}_e$ be such that $C_2$ lies within $C_1$ . If $z_1$ moves on…MediumSingle correct
4 Apr 2026, Shift 1 · Q3Let $z$ be a complex number such that $|z+2|=|z-2|$ and $\arg\left(\frac{z+3}{z-i}\right)=\frac{\pi}{4}$ . Then $|z|^2$ is equal to:MediumSingle correct
2 Apr 2025, Shift 1 · Q2Let $z$ be a complex number such that $|z|=1$ . If $\frac{2+k^2z}{k+\bar{z}}=kz$ , $k\in\mathbf{R}$ , then the maximum distance of $k+ik^2$ …HardSingle correct
7 Apr 2025, Shift 1 · Q2Among the statements (S1) : The set $\{z \in \mathbb{C} - \{-i\} : |z| = 1$ and $\frac{z-i}{z+i}$ is purely real $\}$ contains exactly two…MediumTwo statements
4 Apr 2024, Shift 1 · Q2Let $\alpha$ and $\beta$ be the sum and the product of all the non-zero solutions of the equation $(\bar{z})^2+|z|=0$ , $z \in C$ . Then…MediumSingle correct
5 Apr 2024, Shift 1 · Q2Consider the following two statements : Statement I : For any two non-zero complex numbers $z_1, z_2$ ,…HardTwo statements

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.