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Saturday, 31 October

JEE Main · Maths · Complex Numbers and Quadratic Equations

Locus of Argument Ratio (Circular Arc)

JEE Main asked Locus of Argument Ratio (Circular Arc) 6 times in 6 of the 108 shifts Lumi analysed, in 2021, 2022 and 2026. It belongs to Complex Numbers - Polar Form, in Complex Numbers and Quadratic Equations (Maths). The longest wait between two years asking it was 4 years. In 2021 and 2022 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
6
in 6 shifts
Years
3 of 8
First asked
2021
last in 2026
Pattern
Frequent
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170’200.10’210.07’220’230’240’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 3 in 24 shifts · 2022: 2 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 in 8 shifts · 2026: 1 in 9 shifts.

Shift by shift

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

  • 20261 of 9
  • 20250 of 8
  • 20240 of 18
  • 20230 of 12
  • 20222 of 24
  • 20213 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.

  • Modulus from locus and argument conditions
  • Intersection of circle and argument locus

Difficulty

Easy 0Medium 4Hard 2

1 of the 6 questions had a numerical answer.

Every question

All 6 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 1 · Q3Let zz be a complex number such that ∣z+2∣=∣z−2∣|z+2|=|z-2| and arg⁡(z+3z−i)=π4\arg\left(\frac{z+3}{z-i}\right)=\frac{\pi}{4}. Then ∣z∣2|z|^2 is equal to:MediumSingle correct
  2. 29 Jun 2022, Shift 2 · Q2Let arg⁡(z)\arg(z) represent the principal argument of the complex number zz. Then, ∣z∣=3|z| = 3 and arg⁡(z−1)−arg⁡(z+1)=π4\arg(z - 1) - \arg(z + 1) = \frac{\pi}{4}…MediumSingle correct
  3. 26 Jun 2022, Shift 1 · Q2Let A={z∈C:∣z+1z−1∣<1}A = \left\{z \in \mathbf{C} : \left|\frac{z+1}{z-1}\right| < 1\right\} and…HardSingle correct
  4. 31 Aug 2021, Shift 2 · Q62If zz is a complex number such that z−iz−1\frac{z-i}{z-1} is purely imaginary, then the minimum value of ∣z−(3+3i)∣|z-(3+3i)| is :MediumSingle correct
  5. 31 Aug 2021, Shift 1 · Q82A point zz moves in the complex plane such that arg⁡(z−2z+2)=π4\arg\left(\frac{z-2}{z+2}\right)=\frac{\pi}{4}, then the minimum value of…HardNumerical value
  6. 26 Aug 2021, Shift 1 · Q62The equation arg⁡(z−1z+1)=π4\arg\left(\frac{z-1}{z+1}\right) = \frac{\pi}{4} represents a circle with :MediumSingle correct

Shifts: 26 Aug 2021, Shift 1, 31 Aug 2021, Shift 2, 31 Aug 2021, Shift 1, 26 Jun 2022, Shift 1, 29 Jun 2022, Shift 2, 4 Apr 2026, 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