JEE Main 2023 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 8 April 2023, Shift 2, Maths Q2

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

Let

A = \left\{\theta \in (0, 2\pi) : \frac{1 + 2i\sin\theta}{1 - i\sin\theta} \text{ is purely imaginary}\right\}

. Then the sum of the elements in

A

(1) $2\pi$
(2) $3\pi$
(3) $4\pi$ Official answer
(4) $\pi$

Official answer

Option 3

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Complex Numbers - Polar Form
Idea tested: Purely Real and Imaginary Euler Conditions

Same idea in other shifts

Asked 4× in all

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
8 Apr 2024, Shift 2 · Q7The sum of all possible values of $\theta \in [-\pi, 2\pi]$ , for which $\frac{1 + i\cos\theta}{1 - 2i\cos\theta}$ is purely imaginary, is…MediumSingle correct
11 Apr 2023, Shift 2 · Q21Let $S = \left\{z \in \mathbb{C} - \{i, 2i\} : \frac{z^2 + 8iz - 15}{z^2 - 3iz - 2} \in \mathbb{R}\right\}$ . If…HardNumerical value

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.