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Saturday, 31 October

JEE Main · Maths · Complex Numbers and Quadratic Equations

Roots of z^2 + z + 1 = 0

JEE Main asked Roots of z^2 + z + 1 = 0 2 times in 2 of the 108 shifts Lumi analysed, in 2022 and 2024. It belongs to Roots of Unity, in Complex Numbers and Quadratic Equations (Maths). The longest wait between two years asking it was 2 years.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
2 of 8
First asked
2022
last in 2024
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2022 and 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170’200’210.04’220’230.05’240’250’26

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

Shift by shift

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

  • 20260 of 9
  • 20250 of 8
  • 20241 of 18
  • 20230 of 12
  • 20221 of 24
  • 20210 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Numerical value is the usual form. Skill tested: multi-step.

  • Count common roots of two polynomials
  • Sum of powers of cube root of unity

Difficulty

Easy 0Medium 1Hard 1

1 of the 2 questions had a numerical answer.

Every question

All 2 questions

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

  1. 30 Jan 2024, Shift 2 · Q2If zz is a complex number, then the number of common roots of the equations z1985+z100+1=0z^{1985} + z^{100} + 1 = 0 and z3+2z2+2z+1=0z^3 + 2z^2 + 2z + 1 = 0,…MediumSingle correct
  2. 26 Jun 2022, Shift 2 · Q23If z2+z+1=0z^2 + z + 1 = 0, z∈Cz \in \mathbb{C}, then ∣∑n=115(zn+(−1)n1zn)2∣\left|\sum_{n=1}^{15}\left(z^n + (-1)^n \frac{1}{z^n}\right)^2\right| is equal to ______.HardNumerical value

Shifts: 26 Jun 2022, Shift 2, 30 Jan 2024, Shift 2.

Same topic

Other ideas in Roots of Unity

Roots of Unity has 11 ideas JEE Main has asked; 6 of them came up in more than one question.

Topic analysisChapter analysisStudy this chapterAll repeated ideas