JEE Main Maths · Complex Numbers and Quadratic Equations

Cyclic Powers of Omega Modulo 3

Cyclic Powers of Omega Modulo 3 (Complex Numbers and Quadratic Equations) was asked once in the 42 JEE Main shifts Lumi analysed, in 2025. 1 of the 1 had a numerical answer.

Times asked: 1; in 1 shift
Years: 2025
Usual format: Numerical value; Multi-step
Pattern: New since 2024; asked once so far

How it is asked

N from sum over cube root powers

Difficulty

Easy 0Medium 1Hard 0

Where it sits

Chapter: Complex Numbers and Quadratic Equations. Topic: Roots of Unity, 7 questions over 6 ideas.

The question

Newest first, each with its options and official answer.

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