Complex Number Question 11
Question 11 - 2024 (30 Jan Shift 1)
If $z=x+i y, x y \neq 0$, satisfies the equation $z^{2}+i \bar{z}=0$, then $\left|z^{2}\right|$ is equal to :
(1) 9
(2) 1
(3) 4
(4) $\frac{1}{4}$
Show Answer
Answer (2)
Solution
$z^{2}=-i \overline{z}$
$\left|z^{2}\right|=|iz|$
$\left|z^{2}\right|=|z|$
$|z|^{2}-|z|=0$
$|z|(|z|-1)=0$
$|z|=0$ (not acceptable)
$\therefore|z|=1$
$\therefore|z|^{2}=1$
