JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 22 July 2021, Shift 2, Maths Q78

Question 78 of 90 in this shift, Maths question 18 of 30, Section A.

Let n denote the number of solutions of the equation

z^2+3\bar{z}=0

, where

z

is a complex number. Then the value of

\sum_{k=0}^{\infty}\frac{1}{\mathrm{n}^k}

is equal to :

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

Official answer

Option 4

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Complex Numbers - Polar Form
Idea tested: Polar Conjugate and Inverse

Same idea in other shifts

Asked 5× in all

4 Apr 2024, Shift 1 · Q2Let $\alpha$ and $\beta$ be the sum and the product of all the non-zero solutions of the equation $(\bar{z})^2+|z|=0$ , $z \in C$ . Then…MediumSingle correct
8 Apr 2024, Shift 1 · Q2Let $z$ be a complex number such that $|z+2|=1$ and $\mathrm{Im}\left(\frac{z+1}{z+2}\right)=\frac{1}{5}$ . Then the value of…MediumSingle correct
27 Jul 2022, Shift 1 · Q30Let $S = \{z \in \mathbb{C} : z^2 + \bar{z} = 0\}$ . Then $\sum_{z \in S}\left(\mathrm{Re}(z) + \mathrm{Im}(z)\right)$ is equal to ________.MediumNumerical value
28 Jun 2022, Shift 2 · Q28Sum of squares of modulus of all the complex numbers $z$ satisfying $\bar{z}=iz^2+z^2-z$ is equal to __________.HardNumerical value

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.