JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 29 June 2022, Shift 2, Maths Q2

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

Let

\arg(z)

represent the principal argument of the complex number

z

. Then,

|z| = 3

and

\arg(z - 1) - \arg(z + 1) = \frac{\pi}{4}

intersect

(1)exactly at one point.
(2)exactly at two points.
(3)nowhere.Official answer
(4)at infinitely many points.

Official answer

Option 3

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Complex Numbers - Polar Form
Idea tested: Locus of Argument Ratio (Circular Arc)

Same idea in other shifts

Asked 6× in all

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
26 Jun 2022, Shift 1 · Q2Let $A = \left\{z \in \mathbf{C} : \left|\frac{z+1}{z-1}\right| < 1\right\}$ and…HardSingle correct
26 Aug 2021, Shift 1 · Q62The equation $\arg\left(\frac{z-1}{z+1}\right) = \frac{\pi}{4}$ represents a circle with :MediumSingle correct
31 Aug 2021, Shift 1 · Q82A point $z$ moves in the complex plane such that $\arg\left(\frac{z-2}{z+2}\right)=\frac{\pi}{4}$ , then the minimum value of…HardNumerical value
31 Aug 2021, Shift 2 · Q62If $z$ is a complex number such that $\frac{z-i}{z-1}$ is purely imaginary, then the minimum value of $|z-(3+3i)|$ is :MediumSingle correct

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.