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Saturday, 31 October

JEE Main · Maths · Complex Numbers and Quadratic Equations

Polar Conjugate and Inverse

JEE Main asked Polar Conjugate and Inverse 5 times in 5 of the 108 shifts Lumi analysed, in 2021, 2022 and 2024. It belongs to Complex Numbers - Polar Form, in Complex Numbers and Quadratic Equations (Maths). The longest wait between two years asking it was 2 years. In 2022 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
5
in 5 shifts
Years
3 of 8
First asked
2021
last in 2024
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022 and 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170’200.03’210.07’220’230.09’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 2 in 24 shifts · 2023: 0 in 12 shifts · 2024: 2 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
  • 20242 of 18
  • 20230 of 12
  • 20222 of 24
  • 20211 of 24
  • 20200 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.

  • Real part from modulus and imaginary condition
  • Non-zero solutions of equation in z conjugate and modulus

Difficulty

Easy 0Medium 4Hard 1

2 of the 5 questions had a numerical answer.

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. 8 Apr 2024, Shift 1 · Q2Let zz be a complex number such that ∣z+2∣=1|z+2|=1 and Im(z+1z+2)=15\mathrm{Im}\left(\frac{z+1}{z+2}\right)=\frac{1}{5}. Then the value of…MediumSingle correct
  2. 4 Apr 2024, Shift 1 · Q2Let α\alpha and β\beta be the sum and the product of all the non-zero solutions of the equation (zˉ)2+∣z∣=0(\bar{z})^2+|z|=0, z∈Cz \in C. Then…MediumSingle correct
  3. 28 Jun 2022, Shift 2 · Q28Sum of squares of modulus of all the complex numbers zz satisfying zˉ=iz2+z2−z\bar{z}=iz^2+z^2-z is equal to __________.HardNumerical value
  4. 27 Jul 2022, Shift 1 · Q30Let S={z∈C:z2+zˉ=0}S = \{z \in \mathbb{C} : z^2 + \bar{z} = 0\}. Then ∑z∈S(Re(z)+Im(z))\sum_{z \in S}\left(\mathrm{Re}(z) + \mathrm{Im}(z)\right) is equal to ________.MediumNumerical value
  5. 22 Jul 2021, Shift 2 · Q78Let n denote the number of solutions of the equation z2+3zˉ=0z^2+3\bar{z}=0, where zz is a complex number. Then the value of…MediumSingle correct

Shifts: 22 Jul 2021, Shift 2, 28 Jun 2022, Shift 2, 27 Jul 2022, Shift 1, 4 Apr 2024, Shift 1, 8 Apr 2024, Shift 1.

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