Let z be a complex number such that z + 2 = z - 2 and arg (z + 3/z - i ) = π/4 . Then z 2 is equal to:

Mathematics · Complex Numbers

JEE Main 2026 — 4 April, Morning Shift — Question 26

Let $\mathbf{z}$ 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:

Option A:
9
Correct
Option B:
4
Option C:
5
Option D:
1

Answer: A

Step-by-step solution

$|z+2|=|z-2|$ $\Rightarrow z=0+i y, y \in R$ $\arg \left(\frac{3+i y}{i y-i}\right)=\frac{\pi}{4}$ $\Rightarrow \arg \left(\frac{y}{y-1}+\frac{3 i}{1-y}\right)=\frac{\pi}{4}$ $\Rightarrow \frac{y}{y-1}=\frac{3}{1-y}>0$ $\Rightarrow \mathrm{z}=-3 \mathrm{i}$ $|z|^{2}=9$

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 4 April, Morning Shift
Subject: Mathematics
Chapter: Complex Numbers
Topic: Introduction to Complex Numbers