If $(2 x-y+1)+i(x-2 y-1)=2-3 i$, then the multiplicative inverse of $(x-i y)$ is

If $\cos \alpha$ is the common value of $(-1)^{\frac{1}{4}}$ and $(-i)^{\frac{1}{2}}$ then $\tan \alpha=$

The equation of lowest degree with rational coefficients having roots $\sqrt{3}+\sqrt{2} i$ and $\sqrt{3}-\sqrt{2}$ is

If the point $(x, y)$ satisfies the equation $\frac{x+i(x-2)}{3+i}-i =\frac{2 y+i(1-3 y)}{i-3}$, then $x+y=$