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Saturday, 31 October

JEE Main · Maths · Complex Numbers and Quadratic Equations

Complex Conjugate Roots

JEE Main asked Complex Conjugate Roots 5 times in 4 of the 108 shifts Lumi analysed, in 2020, 2021, 2024 and 2026. It belongs to Quadratic Roots, in Complex Numbers and Quadratic Equations (Maths). The longest wait between two years asking it was 3 years.

Updated 2026-10-24

Times asked
5
in 4 shifts
Years
4 of 8
First asked
2020
last in 2026
Pattern
Frequent
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2024 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.150.30’170.08’200.03’210’220’230.05’240’250.22’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 1 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 1 in 18 shifts · 2025: 0 in 8 shifts · 2026: 2 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 202621 of 9
  • 20250 of 8
  • 20241 of 18
  • 20230 of 12
  • 20220 of 24
  • 20211 of 24
  • 20201 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: multi-step.

  • Sum of moduli over roots
  • Find polynomial from roots then integrate

Difficulty

Easy 2Medium 2Hard 1

Every question was multiple choice.

Every question

All 5 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 4 Apr 2026, Shift 2 · Q2Let S={z∈C:z2+4z+16=0}S=\{z\in\mathbb{C}:z^2+4z+16=0\}. Then ∑z∈S∣z+3 i∣2\sum_{z\in S}|z+\sqrt{3}\,i|^2 is equal to:EasySingle correct
  2. 4 Apr 2026, Shift 2 · Q4If α=1\alpha=1 and β=1+i2\beta=1+i\sqrt{2}, where i=−1i=\sqrt{-1} are two roots of the equation x3+ax2+bx+c=0x^3+ax^2+bx+c=0, a,b,c∈Ra,b,c\in\mathbb{R}, then…MediumSingle correct
  3. 31 Jan 2024, Shift 1 · Q7Let aa be the sum of all coefficients in the expansion of (1−2x+2x2)2023(3−4x2+2x3)2024(1-2x+2x^2)^{2023}(3-4x^2+2x^3)^{2024} and…HardSingle correct
  4. 25 Feb 2021, Shift 2 · Q69If α,β∈R\alpha, \beta \in \mathbf{R} are such that 1−2i1 - 2i (here i2=−1i^2 = -1) is a root of z2+αz+β=0z^2 + \alpha z + \beta = 0, then…EasySingle correct
  5. 8 Jan 2020, Shift 1 · Q52If the equation, x2+bx+45=0x^2+bx+45=0 (b∈Rb\in R) has conjugate complex roots and they satisfy ∣z+1∣=210|z+1|=2\sqrt{10}, then :MediumSingle correct

Shifts: 8 Jan 2020, Shift 1, 25 Feb 2021, Shift 2, 31 Jan 2024, Shift 1, 4 Apr 2026, Shift 2.

Same topic

Other ideas in Quadratic Roots

Quadratic Roots has 22 ideas JEE Main has asked; 13 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas