The square of either of the two imaginary cube roots of unity is:

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 non-real cube root of unity,then $(a + b)(a + b\omega)(a + b\omega^2)$ is equal to:

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

The sum of the least positive arguments of the distinct cube roots of the complex number $(1-i \sqrt{3})$ is

If $\cos \alpha+\cos \beta+\cos \gamma=\sin \alpha+\sin \beta+\sin \gamma=0$,then $\left(\cos ^3 \alpha+\cos ^3 \beta+\cos ^3 \gamma\right)^2+\left(\sin ^3 \alpha+\sin ^3 \beta+\sin ^3 \gamma\right)^2=$