JEE Main 2021 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 26 February 2021, Shift 2, Maths Q82

Question 82 of 90 in this shift, Maths question 22 of 30, Section B.

Let

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 of

|z+1|^2

\alpha+\beta\sqrt{2}

, then the value of

(\alpha+\beta)

is __________.

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

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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
1 Feb 2024, Shift 1 · Q22Let $P=\{z\in\mathbb{C}:|z+2-3i|\leq1\}$ 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…HardNumerical value
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

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.