JEE Main 2021 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 31 August 2021, Shift 1, Maths Q82

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

A point

z

moves in the complex plane such that

\arg\left(\frac{z-2}{z+2}\right)=\frac{\pi}{4}

, then the minimum value of

|z-9\sqrt{2}-2i|^2

is equal to __________.

Official answer

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Complex Numbers - Polar Form
Idea tested: Locus of Argument Ratio (Circular Arc)

Same idea in other shifts

Asked 6× in all

4 Apr 2026, Shift 1 · Q3Let $z$ be a complex number such that $|z+2|=|z-2|$ and $\arg\left(\frac{z+3}{z-i}\right)=\frac{\pi}{4}$ . Then $|z|^2$ is equal to:MediumSingle correct
26 Jun 2022, Shift 1 · Q2Let $A = \left\{z \in \mathbf{C} : \left|\frac{z+1}{z-1}\right| < 1\right\}$ and…HardSingle correct
29 Jun 2022, Shift 2 · Q2Let $\arg(z)$ represent the principal argument of the complex number $z$ . Then, $|z| = 3$ and $\arg(z - 1) - \arg(z + 1) = \frac{\pi}{4}$ …MediumSingle correct
26 Aug 2021, Shift 1 · Q62The equation $\arg\left(\frac{z-1}{z+1}\right) = \frac{\pi}{4}$ represents a circle with :MediumSingle correct
31 Aug 2021, Shift 2 · Q62If $z$ is a complex number such that $\frac{z-i}{z-1}$ is purely imaginary, then the minimum value of $|z-(3+3i)|$ 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.