JEE Main Maths · Complex Numbers and Quadratic Equations

Complex Conjugate Roots

Complex Conjugate Roots (Complex Numbers and Quadratic Equations) was asked 4 times in 3 JEE Main shifts, 2020–2026, out of the 42 shifts Lumi analysed.

Times asked: 4; in 3 shifts
Years: 2020–2026
Usual format: Single correct; Multi-step
Pattern: Frequent; repeats across shifts

How it is asked

Sum of moduli over roots
Find polynomial from roots then integrate

Difficulty

Easy 1Medium 2Hard 1

Where it sits

Chapter: Complex Numbers and Quadratic Equations. Topic: Quadratic Roots, 46 questions over 19 ideas.

All 4 questions

Newest first, each with its options and official answer.

4 Apr 2026, Shift 2 · Q2Let $S=\{z\in\mathbb{C}:z^2+4z+16=0\}$ . Then $\sum_{z\in S}|z+\sqrt{3}\,i|^2$ is equal to:EasySingle correct
4 Apr 2026, Shift 2 · Q4If $\alpha=1$ and $\beta=1+i\sqrt{2}$ , where $i=\sqrt{-1}$ are two roots of the equation $x^3+ax^2+bx+c=0$ , $a,b,c\in\mathbb{R}$ , then…MediumSingle correct
31 Jan 2024, Shift 1 · Q7Let $a$ be the sum of all coefficients in the expansion of $(1-2x+2x^2)^{2023}(3-4x^2+2x^3)^{2024}$ and…HardSingle correct
8 Jan 2020, Shift 1 · Q52If the equation, $x^2+bx+45=0$ ( $b\in R$ ) has conjugate complex roots and they satisfy $|z+1|=2\sqrt{10}$ , then :MediumSingle correct