The product of the distinct $(2n)^{\text{th}}$ roots of $1+i\sqrt{3}$ is equal to:

The common roots of the equations $z^3+2z^2+2z+1=0$ and $z^{2014}+z^{2015}+1=0$ are

If $1, \omega, \omega^2$ are the cube roots of unity,then their product is

If $i = \sqrt{-1}$,then $4 + 5\left(-\frac{1}{2} + \frac{i\sqrt{3}}{2}\right)^{334} + 3\left(-\frac{1}{2} + \frac{i\sqrt{3}}{2}\right)^{365}$ is equal to

Express the following expression in the form $A + iB$: $(\cos 2\theta + i\sin 2\theta )^{ - 5} (\cos 3\theta - i\sin 3\theta )^6 (\sin \theta - i\cos \theta )^3$.

If $\alpha, \beta$ are non-real cube roots of $2$,then $\alpha^6 + \beta^6$ equals