JEE Main Maths · Complex Numbers and Quadratic Equations

Complex Numbers - Polar Form in JEE Main

Name: Complex Numbers - Polar Form: JEE Main previous year questions
Creator: Lumi

Complex Numbers - Polar Form (Maths, Complex Numbers and Quadratic Equations) came 15 times in 15 of the 42 JEE Main shifts Lumi analysed, across 7 distinct ideas. 9 of them came in 2024–26; it was last asked in 2026.

Questions: 15; in 15 shifts
Ideas asked: 7; 3 asked more than once
Numerical answer: 1; 7% of its questions
Pattern: Asked most years; last asked 2026

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 1Medium 11Hard 3

Format

Single correct13 Q
Two statements1 Q
Numerical value1 Q

Ideas inside the topic

7 ideas

Modulus and Argument5 Q
Polar Triangle Inequality Extrema4 Q
Purely Real and Imaginary Euler Conditions2 Q
Polar Conjugate and Inverse1 Q
Locus of Argument Ratio (Circular Arc)1 Q
90-Degree Rotation via 'i'1 Q
Conversion of sin(θ) + i cos(θ)1 Q

Where it sits

Part of Complex Numbers and Quadratic Equations, which had 79 questions in all. Complex Numbers - Polar Form accounts for 19% of them. In Lumi's JEE taxonomy it belongs to Algebra.

Every question

All 15 Complex Numbers - Polar Form questions

Newest first, each with its options and official answer.

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
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
29 Jan 2024, Shift 1 · Q3If $z=\frac{1}{2}-2i$ is such that $|z+1|=\alpha z+\beta(1+i)$ , $i=\sqrt{-1}$ and $\alpha,\beta\in\mathbb{R}$ , then $\alpha+\beta$ is…EasySingle correct
31 Jan 2024, Shift 1 · Q22If $\alpha$ denotes the number of solutions of $|1-i|^x=2^x$ and $\beta=\left(\frac{|z|}{\arg(z)}\right)$ , where…MediumNumerical value
8 Apr 2023, Shift 2 · Q2Let $A = \left\{\theta \in (0, 2\pi) : \frac{1 + 2i\sin\theta}{1 - i\sin\theta} \text{ is purely imaginary}\right\}$ . Then the sum of the…MediumSingle correct
11 Apr 2023, Shift 1 · Q14Let $w_1$ be the point obtained by the rotation of $z_1 = 5 + 4i$ about the origin through a right angle in the anticlockwise direction,…MediumSingle correct
28 Jul 2022, Shift 1 · Q15Let $S_1=\left\{z_1\in\mathbf{C}:|z_1-3|=\frac{1}{2}\right\}$ and $S_2=\{z_2\in\mathbf{C}:|z_2-|z_2+1||=|z_2+|z_2-1||\}$ . Then, for…HardSingle correct
9 Jan 2020, Shift 2 · Q53If $z$ be a complex number satisfying $|\mathrm{Re}(z)|+|\mathrm{Im}(z)|=4$ , then $|z|$ cannot be :MediumSingle correct
2 Sep 2020, Shift 1 · Q53The value of $\left(\frac{1+\sin\frac{2\pi}{9}+i\cos\frac{2\pi}{9}}{1+\sin\frac{2\pi}{9}-i\cos\frac{2\pi}{9}}\right)^{3}$ is :MediumSingle correct
6 Sep 2020, Shift 2 · Q53Let $z=x+iy$ be a non-zero complex number such that $z^2=i|z|^2$ , where $i=\sqrt{-1}$ , then $z$ lies on the :MediumSingle correct