JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 8 April 2024, Shift 1, Maths Q2

Question 2 of 90 in this shift, Maths question 2 of 30, Section A.

Let

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

\left|\mathrm{Re}\left(\overline{z+2}\right)\right|

(1) $\frac{2\sqrt{6}}{5}$ Official answer
(2) $\frac{24}{5}$
(3) $\frac{\sqrt{6}}{5}$
(4) $\frac{1+\sqrt{6}}{5}$

Official answer

Option 1

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
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
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.