JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 28 June 2022, Shift 2, Maths Q28

Question 28 of 90 in this shift, Maths question 28 of 30, Section B.

Sum of squares of modulus of all the complex numbers

z

satisfying

\bar{z}=iz^2+z^2-z

is equal to __________.

Official answer

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
22 Jul 2021, Shift 2 · Q78Let 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…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.