$\cos (x + iy)$ is equal to

If $z=1-\sqrt{3} i$,then $z^3-3 z^2+3 z=$

If $x = 1 + 2i$,then the value of $x^3 + 7x^2 - x + 16$ is

Let $n$ denote the number of solutions of the equation $z^{2}+3 \bar{z}=0$,where $z$ is a complex number. Then the value of $\sum_{k=0}^{\infty} \frac{1}{n^{k}}$ is equal to:

If $z_1$ and $z_2$ are the roots of the equation $x^2+2x+2=0$,then $\frac{-2^{11}(z_1+1+3i)^{11}}{2^5(z_2+1-3i)^{11}}$ is equal to

If $\frac{1-10 i \cos \theta}{1-10 \sqrt{3} i \sin \theta}$ is purely real,then one of the values of $\theta$ is