If $x = a$,$y = b\omega$,and $z = c\omega^2$,where $\omega$ is a complex cube root of unity,then $\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = \dots$

The number of real values of $(-1-\sqrt{3} i)^{3/4}$ is

If the least positive integer $n$ satisfying the equation $\left(\frac{\sqrt{3}+i}{\sqrt{3}-i}\right)^{n}=-1$ is $p$ and the least positive integer $m$ satisfying the equation $\left(\frac{1-\sqrt{3} i}{1+\sqrt{3} i}\right)^m=\operatorname{cis} \frac{2 \pi}{3}$ is $q$,then $\sqrt{p^2+q^2}=$

The number of distinct solutions of the equation $x^{11}-x^7+x^4-1=0$ is

The cube roots of unity are the vertices of a/an ......... which is inscribed in a circle of unit radius,with its centre at the origin.

If $n, K \in N$ such that $n \neq 3K$,then $(\sqrt{3}+i)^{2n} + (\sqrt{3}-i)^{2n} = $