JEE Main Maths · Complex Numbers and Quadratic Equations

Roots of Unity in JEE Main

Name: Roots of Unity: JEE Main previous year questions
Creator: Lumi

Roots of Unity (Maths, Complex Numbers and Quadratic Equations) came 7 times in 7 of the 42 JEE Main shifts Lumi analysed, across 6 distinct ideas. 4 of them came in 2024–26; it was last asked in 2025.

Questions: 7; in 7 shifts
Ideas asked: 6; 1 asked more than once
Numerical answer: 2; 29% of its questions
Pattern: Asked most years; last asked 2025

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 0Medium 7Hard 0

Format

Single correct5 Q
Numerical value2 Q

Ideas inside the topic

6 ideas

Equilateral Triangle Condition via Omega2 Q
Cyclic Powers of Omega Modulo 31 Q
Evaluating Determinants with Cube Roots1 Q
Periodicity of Omega Powers1 Q
Roots of z^2 + z + 1 = 01 Q
Sum of p-th Powers of Roots1 Q

Where it sits

Part of Complex Numbers and Quadratic Equations, which had 79 questions in all. Roots of Unity accounts for 9% of them. In Lumi's JEE taxonomy it belongs to Algebra.

Some questions sit in other chapters too: Determinants, Matrices.

Every question

All 7 Roots of Unity questions

Newest first, each with its options and official answer.

3 Apr 2025, Shift 2 · Q5If $z_1, z_2, z_3 \in \mathbb{C}$ are the vertices of an equilateral triangle, whose centroid is $z_0$ , then…MediumSingle correct
4 Apr 2025, Shift 2 · Q21If $\alpha$ is a root of the equation $x^2+x+1=0$ and $\sum_{k=1}^{n}\left(\alpha^k+\frac{1}{\alpha^k}\right)^2=20$ , then n is equal to…MediumNumerical value
8 Apr 2025, Shift 2 · Q5Let $\alpha$ be a solution of $x^2 + x + 1 = 0$ , and for some $a$ and $b$ in $\mathbb{R}$ ,…MediumSingle correct
30 Jan 2024, Shift 2 · Q2If $z$ is a complex number, then the number of common roots of the equations $z^{1985} + z^{100} + 1 = 0$ and $z^3 + 2z^2 + 2z + 1 = 0$ ,…MediumSingle correct
25 Jul 2022, Shift 1 · Q2If $\alpha,\ \beta,\ \gamma,\ \delta$ are the roots of the equation $x^4+x^3+x^2+x+1=0$ , then…MediumSingle correct
18 Mar 2021, Shift 1 · Q81Let $z_1, z_2$ be the roots of the equation $z^2+az+12=0$ and $z_1, z_2$ form an equilateral triangle with origin. Then, the value of…MediumNumerical value
2 Apr 2017 (offline) · Q63Let $\omega$ be a complex number such that $2\omega+1=z$ where $z=\sqrt{-3}$ . If…MediumSingle correct