Mathematics · Complex Numbers

JEE Main 2024 — 30 January, Shift 1 — Question 3

If $z=x+i y, x y \neq 0$ , satisfies the equation $z^{2}+i \bar{z}=0$ , then $|z|^{2}$ is equal to :

Answer: B

$z^{2}=-i \bar{z}$

$\left|z^{2}\right|=|i \bar{z}|$

$\left|z^{2}\right|=|z|$

$|z|^{2}-|z|=0$

$|z|(|z|-1)=0$

$|z|=0$ (not acceptable)

$\therefore|z|=1$

$\therefore|z|^{2}=1$

Answer key and solution verified before publishing.

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.