The value of $(1 - \omega + \omega^2)(1 - \omega^2 + \omega)^6$,where $\omega, \omega^2$ are the complex cube roots of unity.

If $1, \omega, \omega^2, \ldots, \omega^8$ are the roots of the equation $x^9-1=0$,then $\sum_{r=1}^8 \left(\omega^r\right)^{99} =$

If $|x+iy|=\sqrt{x^2+y^2}$,then $|(1-\sqrt{3}i)^9+(\sqrt{3}+i)^9|=$

If $\omega$ is a non-real cube root of unity,then the value of $\cos \left[ \left\{ (1-\omega)(1-\omega^2) + (2-\omega)(2-\omega^2) + \dots + (2017-\omega)(2017-\omega^2) \right\} \cdot \frac{\pi}{2017} \right]$ is -

If $\alpha, \beta$ are the roots of the equation $x^2+x+1=0$,then $(\alpha+\beta)^2+(\alpha^2+\beta^2)^2+(\alpha^3+\beta^3)^2+\ldots+(\alpha^{12}+\beta^{12})^2=$

One of the values of $(\sqrt{3}-i)^{\frac{1}{6}}$ is