JEE Main 2020 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 6 September 2020, Shift 2, Maths Q53

Question 53 of 75 in this shift, Maths question 3 of 25.

Let

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 :

(1)imaginary axis
(2)real axis
(3)line, $y=x$ Official answer
(4)line, $y=-x$

Official answer

Option 3

NTA final key (Sep 2020).

Chapter: Complex Numbers and Quadratic Equations
Topic: Complex Numbers - Polar Form
Idea tested: Modulus and Argument

Same idea in other shifts

Asked 5× in all

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

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.