If $1, \omega, \omega^2$ are the three cube roots of unity,then $(3 + \omega^2 + \omega^4)^6 = $

Let ${\omega _n} = \cos \left( {\frac{{2\pi }}{n}} \right) + i\sin \left( {\frac{{2\pi }}{n}} \right)$ and ${i^2} = -1$. Then $(x + y{\omega _3} + z{\omega _3}^2)(x + y{\omega _3}^2 + z{\omega _3})$ is equal to:

If $y = \cos \theta + i\sin \theta$,then the value of $y + \frac{1}{y}$ is

If $\alpha$ is a non-real root of the equation $x^6-1=0$,then $\frac{\alpha^2+\alpha^3+\alpha^4+\alpha^5}{\alpha+1} = $

$A$ value of $n$ such that $\left(\frac{\sqrt{3}}{2}+\frac{i}{2}\right)^n=1$ is

If $\omega$ represents a complex cube root of unity,then $\left(1+\frac{1}{\omega}\right)\left(1+\frac{1}{\omega^2}\right)+\left(2+\frac{1}{\omega}\right)\left(2+\frac{1}{\omega^2}\right)+\ldots+\left(n+\frac{1}{\omega}\right)\left(n+\frac{1}{\omega^2}\right)=$