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Saturday, 31 October

JEE Main · Maths · Complex Numbers and Quadratic Equations

De Moivre's Theorem for Integer Powers

JEE Main asked De Moivre's Theorem for Integer Powers 4 times in 3 of the 108 shifts Lumi analysed, all in 2021. It belongs to Complex Numbers - Polar Form, in Complex Numbers and Quadratic Equations (Maths). In 2021 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
4
in 3 shifts
Years
1 of 8
First asked
2021
the only year
Pattern
Gone quiet
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170’200.14’210’220’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 4 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 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
  • 20240 of 18
  • 20230 of 12
  • 20220 of 24
  • 202123 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.

  • Form quadratic from real and imaginary parts of power
  • Least integer power making complex expression real positive

Difficulty

Easy 0Medium 4Hard 0

3 of the 4 questions had a numerical answer.

Every question

All 4 questions

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

  1. 24 Feb 2021, Shift 2 · Q84Let i=−1i=\sqrt{-1}. If (−1+i3)21(1−i)24+(1+i3)21(1+i)24=k\frac{(-1+i\sqrt{3})^{21}}{(1-i)^{24}}+\frac{(1+i\sqrt{3})^{21}}{(1+i)^{24}}=k, and n=[∣k∣]\mathrm{n}=[|k|] be the…MediumNumerical value
  2. 26 Aug 2021, Shift 2 · Q62If (3+i)100=299(p+iq)(\sqrt{3}+i)^{100}=2^{99}(\mathrm{p}+i\mathrm{q}), then p and q are roots of the equation :MediumSingle correct
  3. 26 Aug 2021, Shift 2 · Q88The least positive integer n such that (2i)n(1−i)n−2\frac{(2i)^{\mathrm{n}}}{(1-i)^{\mathrm{n}-2}}, i=−1i=\sqrt{-1}, is a positive integer, is…MediumNumerical value
  4. 4 Aug 2021, Shift 2 · Q81If z=3−i2z=\frac{\sqrt3-i}{2} and (z95+i95)94=zn(z^{95}+i^{95})^{94}=z^n, then the minimum positive integral value of ‘nn’ is ________ .MediumNumerical value

Shifts: 24 Feb 2021, Shift 2, 4 Aug 2021, Shift 2, 26 Aug 2021, Shift 2.

Same topic

Other ideas in Complex Numbers - Polar Form

Complex Numbers - Polar Form has 20 ideas JEE Main has asked; 9 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas