JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 27 June 2022, Shift 1, Maths Q1

Question 1 of 90 in this shift, Maths question 1 of 30, Section A.

The area of the polygon, whose vertices are the non-real roots of the equation

\bar{z} = iz^2

is :

(1) $\frac{3\sqrt{3}}{4}$ Official answer
(2) $\frac{3\sqrt{3}}{2}$
(3) $\frac{3}{2}$
(4) $\frac{3}{4}$

Official answer

Option 1

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Roots of Unity
Idea tested: Roots of z^n = z_0

Same topic in other shifts

All Roots of Unity questions

3 Apr 2025, Shift 2 · Q5If $z_1, z_2, z_3 \in \mathbb{C}$ are the vertices of an equilateral triangle, whose centroid is $z_0$ , then…MediumSingle correct
4 Apr 2025, Shift 2 · Q21If $\alpha$ is a root of the equation $x^2+x+1=0$ and $\sum_{k=1}^{n}\left(\alpha^k+\frac{1}{\alpha^k}\right)^2=20$ , then n is equal to…MediumNumerical value
8 Apr 2025, Shift 2 · Q5Let $\alpha$ be a solution of $x^2 + x + 1 = 0$ , and for some $a$ and $b$ in $\mathbb{R}$ ,…MediumSingle correct
27 Jan 2024, Shift 1 · Q21If $\alpha$ satisfies the equation $x^2+x+1=0$ and $(1+\alpha)^7=A+B\alpha+C\alpha^2$ , $A, B, C\geq 0$ , then $5(3A-2B-C)$ is equal to…MediumNumerical value
30 Jan 2024, Shift 2 · Q2If $z$ is a complex number, then the number of common roots of the equations $z^{1985} + z^{100} + 1 = 0$ and $z^3 + 2z^2 + 2z + 1 = 0$ ,…MediumSingle correct
25 Jul 2022, Shift 1 · Q2If $\alpha,\ \beta,\ \gamma,\ \delta$ are the roots of the equation $x^4+x^3+x^2+x+1=0$ , then…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 108 of the 174 JEE Main shifts held from 2017 to 2026.