If $i^2 = -1$,then $(1 + \sqrt{3} i)^{2022} - (\sqrt{3} - i)^{2022} = $

Two values of $(-8-8 \sqrt{3} i)^{1/4}$ are

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

If $\alpha$ and $\beta$ are the roots of $x^{2}+x+1=0$,then $\alpha^{16}+\beta^{16}$ is equal to

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

Let $a = \cos 1^{\circ}$ and $b = \sin 1^{\circ}$. We say that a real number is algebraic if it is a root of a polynomial with integer coefficients. Then,