If $\alpha, \beta$ are non-real cube roots of $2$,then $\alpha^6 + \beta^6$ equals

When $n=8$,$(\sqrt{3}+i)^n+(\sqrt{3}-i)^n=$

If $1, \omega, \omega^2$ are the cube roots of unity,then $\omega^2(1 + \omega)^3 - (1 + \omega^2)\omega = $

If $\alpha$ and $\beta$ are the complex cube roots of unity,then $\alpha^3+\beta^3+\alpha^{-2} \times \beta^{-2}$ is equal to

If $\omega$ is a complex cube root of unity and $a, b, c$ are distinct real numbers,then $\frac{a+b \omega+c \omega^2}{c+a \omega+b \omega^2}+\frac{a+b \omega+c \omega^2}{b+c \omega+a \omega^2} = $

The roots of the equation $x^3-3x^2+3x+7=0$ are $\alpha, \beta, \gamma$ and $\omega, \omega^2$ are complex cube roots of unity. If the terms containing $x^2$ and $x$ are missing in the transformed equation when each one of these roots is decreased by $h$,then $\frac{\alpha-h}{\beta-h}+\frac{\beta-h}{\gamma-h}+\frac{\gamma-h}{\alpha-h}=$