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Saturday, 31 October

JEE Main · Maths · Complex Numbers and Quadratic Equations

Modulus and Argument

JEE Main asked Modulus and Argument 13 times in 13 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2023 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 1 year. In 2020, 2022 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
13
in 13 shifts
Years
5 of 8
First asked
2020
last in 2024
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022, 2023 and 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.150.30’170.25’200.03’210.07’220.07’230.28’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 3 in 12 shifts · 2021: 1 in 24 shifts · 2022: 2 in 24 shifts · 2023: 1 in 12 shifts · 2024: 6 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
  • 20246 of 18
  • 20231 of 12
  • 20222 of 24
  • 20211 of 24
  • 20203 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.

  • Distance of point from complex modulus and argument
  • Unknown real constants from complex equation

Difficulty

Easy 1Medium 8Hard 4

2 of the 13 questions had a numerical answer.

Every question

All 13 questions

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

  1. 31 Jan 2024, Shift 1 · Q22If α\alpha denotes the number of solutions of ∣1−i∣x=2x|1-i|^x=2^x and β=(∣z∣arg⁡(z))\beta=\left(\frac{|z|}{\arg(z)}\right), where…MediumNumerical value
  2. 30 Jan 2024, Shift 1 · Q2If z=x+iy, xy≠0z=x+iy,\ xy\neq0, satisfies the equation z2+izˉ=0z^2+i\bar{z}=0, then ∣z2∣|z^2| is equal to :MediumSingle correct
  3. 29 Jan 2024, Shift 1 · Q3If z=12−2iz=\frac{1}{2}-2i is such that ∣z+1∣=αz+β(1+i)|z+1|=\alpha z+\beta(1+i), i=−1i=\sqrt{-1} and α,β∈R\alpha,\beta\in\mathbb{R}, then α+β\alpha+\beta is…EasySingle correct
  4. 1 Feb 2024, Shift 1 · Q1Let S={z∈C:∣z−1∣=1S=\{z\in\mathbb{C}:|z-1|=1 and (2−1)(z+zˉ)−i(z−zˉ)=22}(\sqrt{2}-1)(z+\bar{z})-i(z-\bar{z})=2\sqrt{2}\}. Let z1,z2∈Sz_1, z_2\in S be such that…HardSingle correct
  5. 6 Apr 2024, Shift 2 · Q3If z1,z2z_1, z_2 are two distinct complex number such that ∣z1−2z212−z1z2ˉ∣=2\left|\frac{z_1-2z_2}{\frac{1}{2}-z_1\bar{z_2}}\right|=2, thenHardSingle correct
  6. 5 Apr 2024, Shift 1 · Q2Consider the following two statements : Statement I : For any two non-zero complex numbers z1,z2z_1, z_2,…HardTwo statements
  7. 8 Apr 2023, Shift 1 · Q2If for z=α+iβz=\alpha+i\beta, ∣z+2∣=z+4(1+i)|z+2|=z+4(1+i), then α+β\alpha+\beta and αβ\alpha\beta are the roots of the equationMediumSingle correct
  8. 30 Jul 2022, Shift 2 · Q62Let z1=1+2iz_1 = 1 + 2i, z2=2+iz_2 = 2 + i, 1z1+1z2=6w\frac{1}{z_1}+\frac{1}{z_2}=\frac{6}{w}, and z=iw2−w‾z = \frac{iw}{2-\overline{w}}. Consider the statements…MediumTwo statements
  9. 28 Jul 2022, Shift 2 · Q88Let z=a+ib, b≠0z=a+ib,\ b\neq 0 be complex numbers satisfying z2=zˉ⋅21−∣z∣z^2=\bar{z}\cdot 2^{1-|z|}. Then the least value of n∈Nn\in\mathbb{N}, such that…HardNumerical value
  10. 4 Aug 2021, Shift 1 · Q62If z=x+iyz=x+iy and ω=z−13(z−2)\omega=\frac{z-1}{3(z-2)}, then the set of points zz satisfying ∣z∣=1=∣ω∣|z|=1=|\omega| containsMediumSingle correct
  11. 6 Sep 2020, Shift 2 · Q53Let z=x+iyz=x+iy be a non-zero complex number such that z2=i∣z∣2z^2=i|z|^2, where i=−1i=\sqrt{-1}, then zz lies on the :MediumSingle correct
  12. 9 Jan 2020, Shift 2 · Q53If zz be a complex number satisfying ∣Re(z)∣+∣Im(z)∣=4|\mathrm{Re}(z)|+|\mathrm{Im}(z)|=4, then ∣z∣|z| cannot be :MediumSingle correct
  13. 9 Jan 2020, Shift 1 · Q53Let zz be a complex number such that ∣z−iz+2i∣=1\left|\frac{z-i}{z+2i}\right|=1 and ∣z∣=52|z|=\frac{5}{2}. Then the value of ∣z+3i∣|z+3i| is :MediumSingle correct

Shifts: 9 Jan 2020, Shift 2, 9 Jan 2020, Shift 1, 6 Sep 2020, Shift 2, 4 Aug 2021, Shift 1, 28 Jul 2022, Shift 2, 30 Jul 2022, Shift 2, 8 Apr 2023, Shift 1, 29 Jan 2024, Shift 1, 30 Jan 2024, Shift 1, 31 Jan 2024, Shift 1, 1 Feb 2024, Shift 1, 5 Apr 2024, Shift 1, 6 Apr 2024, 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