If $\omega$ is a complex cube root of unity,then $225+(3 \omega+8 \omega^2)^2+(3 \omega^2+8 \omega)^2$ is equal to:

If $\omega$ is a complex cube root of unity and $x = \omega^2 - \omega + 2$,then:

If $\cos \alpha + \cos \beta + \cos \gamma = 0$ and $\sin \alpha + \sin \beta + \sin \gamma = 0$,then $\cos 3\alpha + \cos 3\beta + \cos 3\gamma$ equals to

One of the values of $(\sqrt{3}-i)^{\frac{2}{5}}$ is

One of the roots of the equation $(x+1)^4 + 81 = 0$ is

The product $(1 - \omega + {\omega ^2})(1 - {\omega ^2} + {\omega ^4})(1 - {\omega ^4} + {\omega ^8}) \dots$ up to $2n$ factors is: