JEE Main Maths · Complex Numbers and Quadratic Equations

Modulus and Argument

Modulus and Argument (Complex Numbers and Quadratic Equations) was asked 5 times in 5 JEE Main shifts, 2020–2024, out of the 42 shifts Lumi analysed. 1 of the 5 had a numerical answer.

Times asked: 5; in 5 shifts
Years: 2020–2024
Usual format: Single correct; Application
Pattern: Occasional; repeats across shifts

How it is asked

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

Difficulty

Easy 1Medium 3Hard 1

Where it sits

Chapter: Complex Numbers and Quadratic Equations. Topic: Complex Numbers - Polar Form, 15 questions over 7 ideas.

All 5 questions

Newest first, each with its options and official answer.

6 Apr 2024, Shift 2 · Q3If $z_1, z_2$ are two distinct complex number such that $\left|\frac{z_1-2z_2}{\frac{1}{2}-z_1\bar{z_2}}\right|=2$ , thenHardSingle correct
29 Jan 2024, Shift 1 · Q3If $z=\frac{1}{2}-2i$ is such that $|z+1|=\alpha z+\beta(1+i)$ , $i=\sqrt{-1}$ and $\alpha,\beta\in\mathbb{R}$ , then $\alpha+\beta$ is…EasySingle correct
31 Jan 2024, Shift 1 · Q22If $\alpha$ denotes the number of solutions of $|1-i|^x=2^x$ and $\beta=\left(\frac{|z|}{\arg(z)}\right)$ , where…MediumNumerical value
9 Jan 2020, Shift 2 · Q53If $z$ be a complex number satisfying $|\mathrm{Re}(z)|+|\mathrm{Im}(z)|=4$ , then $|z|$ cannot be :MediumSingle correct
6 Sep 2020, Shift 2 · Q53Let $z=x+iy$ be a non-zero complex number such that $z^2=i|z|^2$ , where $i=\sqrt{-1}$ , then $z$ lies on the :MediumSingle correct