JEE Main 2024 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 1 February 2024, Shift 1, Maths Q22

Question 22 of 90 in this shift, Maths question 22 of 30, Section B.

Let

P=\{z\in\mathbb{C}:|z+2-3i|\leq1\}

and

Q=\{z\in\mathbb{C}:z(1+i)+\bar{z}(1-i)\leq-8\}

. Let in

P\cap Q

|z-3+2i|

be maximum and minimum at

z_1

and

z_2

respectively. If

|z_1|^2+2|z_2|^2=\alpha+\beta\sqrt{2}

, where

\alpha,\beta

are integers, then

\alpha+\beta

equals __________.

Official answer

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Complex Numbers - Polar Form
Idea tested: Polar Triangle Inequality Extrema

Same idea in other shifts

Asked 8× in all

2 Apr 2026, Shift 2 · Q2Let the circles $C_1: |z| = r$ and $C_2: |z - 3 - 4i| = 5, z \in \mathbb{C}_e$ be such that $C_2$ lies within $C_1$ . If $z_1$ moves on…MediumSingle correct
2 Apr 2025, Shift 1 · Q2Let $z$ be a complex number such that $|z|=1$ . If $\frac{2+k^2z}{k+\bar{z}}=kz$ , $k\in\mathbf{R}$ , then the maximum distance of $k+ik^2$ …HardSingle correct
9 Apr 2024, Shift 2 · Q2Let $z$ be a complex number such that the real part of $\frac{z-2i}{z+2i}$ is zero. Then, the maximum value of $|z-(6+8i)|$ is equal toMediumSingle correct
25 Jul 2022, Shift 2 · Q1For $z \in \mathbb{C}$ if the minimum value of $\left(\left|z-3\sqrt{2}\right|+\left|z-p\sqrt{2}i\right|\right)$ is $5\sqrt{2}$ , then a…MediumSingle correct
28 Jul 2022, Shift 1 · Q15Let $S_1=\left\{z_1\in\mathbf{C}:|z_1-3|=\frac{1}{2}\right\}$ and $S_2=\{z_2\in\mathbf{C}:|z_2-|z_2+1||=|z_2+|z_2-1||\}$ . Then, for…HardSingle correct
29 Jul 2022, Shift 2 · Q1If $z\neq 0$ be a complex number such that $\left|z-\frac{1}{z}\right|=2$ , then the maximum value of $|z|$ is :MediumSingle correct
26 Feb 2021, Shift 2 · Q82Let $z$ be those complex numbers which satisfy $|z+5| \le 4$ and $z(1+i)+\overline{z}(1-i) \ge -10$ , $i=\sqrt{-1}$ . If the maximum value…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.