In argand plane, no value of $\sqrt[3]{1-i \sqrt{3}}$ lie in

If $\frac{2+3 i}{i-2}-\frac{4 i-3}{3+4 i}=x+i y$, then $3 x+y=$

Let $z=x+i y$ and $P(x, y)$ be a point on the argand plane. If $z$ satisfies the condition $\arg \left(\frac{z-3 i}{z+2 i}\right)=\frac{\pi}{4}$, then the locus of $P$ is

If $\omega$ is a complex cube root of unity and $x=\omega^2-\omega+2$, then