JEE Main 2026 · 4 Apr · Shift 1 · Mathematics Q3

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MathematicsSingle correct+4 / -1Question 3 of 75

Let $z$ be a complex number such that $|z+2|=|z-2|$ and $\arg\left(\dfrac{z+3}{z-i}\right)=\dfrac\pi4$ . Then $|z|^2$ is equal to:

Answer and worked solution

Official answer: A

First condition. $|z+2|=|z-2|$ puts $z$ on the imaginary axis: $z=iy$ .

Argument. $\dfrac{3+iy}{i(y-1)}=\dfrac{y-3i}{y-1}$ . An argument of $\frac\pi4$ needs equal, positive real and imaginary parts: $y=-3$ , giving $\frac34+\frac34i$ ✓.

Value. $|z|^2=9$ .

(A)

Topics:Modulus and argument Geometry in the complex plane

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JEE Main 2026 · 4 Apr · Shift 1, Mathematics question 3