Jee Main 2024 30 01 2024 Shift1 - Question12
Question 12
For a non-zero complex number $z$ satisfying $z^{2}+i \bar{z}=0$, then value of $|z|^{2}$ is
(1) 1
(2) 2
(3) 3
(4) 4
Show Answer
Answer: (1)
Solution:
$z^{2}=-i \bar{z}$
$\left|z^{2}\right|=|-i \bar{z}|$
$\left|z^{2}\right|=|z|$
$|z|^{2}-|z|=0$
$|z|(|z|-1)=0$
$|z|=0$ (not acceptable)
$\therefore|z|=1$
$\therefore|z|^{2}=1$
BETA
