If $i{z^4} + 1 = 0$,then $z$ can take the value

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

If $\omega$ is a non-real cube root of unity and $x = \omega^2 - \omega - 3$,then the value of $x^4 + 6x^3 + 10x^2 - 12x - 19$ is

The roots of $(2 - 2i)^{1/3}$ are

The value of $\frac{a + b\omega + c\omega^2}{b + c\omega + a\omega^2} + \frac{a + b\omega + c\omega^2}{c + a\omega + b\omega^2}$ is

If $\theta = \frac{\pi}{6}$,then the $10^{th}$ term of the series $1 + (\cos \theta + i \sin \theta) + (\cos \theta + i \sin \theta)^2 + (\cos \theta + i \sin \theta)^3 + \ldots$ is equal to: