If $z = 2 + 3i$,then $z^{5} + (\bar{z})^{5}$ is equal to:

If $(x-iy)^{\frac{1}{3}} = a+ib$,then $\frac{ax-by}{a-b} = $

If $a, b, c$ are non-zero real numbers with $c \neq 1$ such that $a^2+b^2+c^2=c$ and if $\alpha=\frac{a+i b}{1-c}$,then $a^2+b^2=$

If $f(x)$ is a polynomial of degree $n$ with rational coefficients and $1+2i, 2-\sqrt{3}$ and $5$ are three roots of $f(x)=0$,then the least value of $n$ is

$\left(\cos \frac{\pi}{2}+i \sin \frac{\pi}{2}\right) \times \left(\cos \frac{\pi}{4}+i \sin \frac{\pi}{4}\right) \times \left(\cos \frac{\pi}{8}+i \sin \frac{\pi}{8}\right) \times \ldots \infty =$

The equation whose solutions are the non-zero solutions of the equation $\bar{z}=i z^2$ is: