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

If $\omega$ is a complex cube root of unity,then for a positive integral value of $n$,the product $\omega \cdot \omega^2 \cdot \omega^3 \cdots \omega^n$ will be:

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 $\omega$ is a complex cube root of unity,then $(x - y)(x\omega - y)(x\omega^2 - y) = $

If $1, \alpha_1, \alpha_2, \ldots, \alpha_{n-1}$ are the $n^{\text{th}}$ roots of unity,then $\sum_{1 \leq i < j \leq n-1} \alpha_i \alpha_j =$

If $z$ is a non-real root of $x^7=1$,then $1+3z+5z^2+7z^3+9z^4+11z^5+13z^6=$