If [z=x+i y, x y 0], satisfies the equation [z^2+i z=0], then [|z^2|] is equal to :

Question

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 :

Accepted Answer

$$\begin{aligned}
& z^2=-i \bar{z} \
& \left|z^2\right|=|i \bar{z}| \
& \left|z^2\right|=|z| \
& |z|^2-|z|=0 \
& |z|(|z|-1)=0 \
& |z|=0 \text { (not acceptable) } \
& \therefore|z|=1 \
& \therefore|z|^2=1
\end{aligned}$$

Solutions · 1