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

If $\omega$ is the complex cube root of unity,then the value of $\left(3+5 \omega+3 \omega^2\right)^2+\left(3+3 \omega+5 \omega^2\right)^2$ is:

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

If $\omega$ is an imaginary cube root of unity,$(1 + \omega - \omega^2)^7$ equals

The least positive integral value of $n$ such that $\left[\frac{1+\sin \frac{2 \pi}{9}+i \cos \frac{2 \pi}{9}}{1+\sin \frac{2 \pi}{9}-i \cos \frac{2 \pi}{9}}\right]^n=1$ is

If $2x = -1 + \sqrt{3}i$,then the value of $(1 - x^2 + x)^6 - (1 - x + x^2)^6$ is