If $z=x+i y$ and $x^2+y^2=1$, then $\frac{1+x+i y}{1+x-i y}=$

If $x^6=(\sqrt{3}-i)^5$, then the product of all of its roots is

If $z=x+i y$ and if the point $P$ in the argand diagram represents $z$, then the locus of the point $P$ satisfying the equation $2|z-2-3 i|=3|z+i-2|$ is a circle with centre