JEE Main 2026 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 4 April 2026, Shift 1, Maths Q3

Question 3 of 75 in this shift, Maths question 3 of 25, Section A.

Let

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:

(1) $9$ Official answer
(2) $4$
(3) $5$
(4) $1$

Official answer

Option 1

NTA final key.

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

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
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
6 Apr 2024, Shift 2 · Q3If $z_1, z_2$ are two distinct complex number such that $\left|\frac{z_1-2z_2}{\frac{1}{2}-z_1\bar{z_2}}\right|=2$ , thenHardSingle correct
8 Apr 2024, Shift 1 · Q2Let $z$ be a complex number such that $|z+2|=1$ and $\mathrm{Im}\left(\frac{z+1}{z+2}\right)=\frac{1}{5}$ . Then the value of…MediumSingle correct
9 Apr 2024, Shift 2 · Q2Let $z$ be a complex number such that the real part of $\frac{z-2i}{z+2i}$ is zero. Then, the maximum value of $|z-(6+8i)|$ is equal toMediumSingle 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 42 of the 174 JEE Main shifts held from 2017 to 2026.