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

By taking $\sqrt{a \pm i b}=x \pm i y, x>0$, if we get $\frac{\sqrt{21+12 \sqrt{2 i}}}{\sqrt{21-12 \sqrt{2 i}}}=a+i b$, then $\frac{b}{a}=$

Two values of $(-8-8 \sqrt{3} i)^{1 / 4}$ are

If $z$ and $w$ are two non-zero complex numbers such that $|z w|=1$ and $\arg z-\arg w=\frac{\pi}{2}$, then $\bar{z} w=$