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Saturday, 31 October

JEE Main · Maths · Complex Numbers and Quadratic Equations

Purely Real and Imaginary Euler Conditions

JEE Main asked Purely Real and Imaginary Euler Conditions 4 times in 4 of the 108 shifts Lumi analysed, in 2023, 2024 and 2025. It belongs to Complex Numbers - Polar Form, in Complex Numbers and Quadratic Equations (Maths). The longest wait between two years asking it was 1 year. In 2023 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
4
in 4 shifts
Years
3 of 8
First asked
2023
last in 2025
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2023, 2024 and 2025. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200’210’220.14’230.05’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 0 in 24 shifts · 2023: 2 in 12 shifts · 2024: 1 in 18 shifts · 2025: 1 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
  • 20251 of 8
  • 20241 of 18
  • 20232 of 12
  • 20220 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

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

  • Statement i/ii on locus of complex numbers
  • Sum of angles making complex quotient imaginary

Difficulty

Easy 0Medium 3Hard 1

1 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. 7 Apr 2025, Shift 1 · Q2Among the statements (S1) : The set {z∈C−{−i}:∣z∣=1\{z \in \mathbb{C} - \{-i\} : |z| = 1 and z−iz+i\frac{z-i}{z+i} is purely real}\} contains exactly two…MediumTwo statements
  2. 8 Apr 2024, Shift 2 · Q7The sum of all possible values of θ∈[−π,2π]\theta \in [-\pi, 2\pi], for which 1+icos⁡θ1−2icos⁡θ\frac{1 + i\cos\theta}{1 - 2i\cos\theta} is purely imaginary, is…MediumSingle correct
  3. 11 Apr 2023, Shift 2 · Q21Let S={z∈C−{i,2i}:z2+8iz−15z2−3iz−2∈R}S = \left\{z \in \mathbb{C} - \{i, 2i\} : \frac{z^2 + 8iz - 15}{z^2 - 3iz - 2} \in \mathbb{R}\right\}. If…HardNumerical value
  4. 8 Apr 2023, Shift 2 · Q2Let A={θ∈(0,2π):1+2isin⁡θ1−isin⁡θ is purely imaginary}A = \left\{\theta \in (0, 2\pi) : \frac{1 + 2i\sin\theta}{1 - i\sin\theta} \text{ is purely imaginary}\right\}. Then the sum of the…MediumSingle correct

Shifts: 8 Apr 2023, Shift 2, 11 Apr 2023, Shift 2, 8 Apr 2024, Shift 2, 7 Apr 2025, 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