If $1, \omega, \omega^2$ are the cube roots of unity,then the value of $(x+y)^2+(x \omega+y \omega^2)^2+(x \omega^2+y \omega)^2$ is

The sum of the $162^{\text{th}}$ power of the roots of the equation $x^{3}-2x^{2}+2x-1=0$ is

If $n$ is a positive integer, then $(1 + i\sqrt{3})^{2n} + (1 - i\sqrt{3})^{2n}$ is equal to .........

If $\alpha, \beta$ are the roots of the equation $x^2-2x+2=0$,then $\alpha^{2020}+\beta^{2020}=$

Let $1, \omega$ and $\omega^2$ be the cube roots of unity. What is the value of $(1-\omega+\omega^{-1})^5-2(1+\omega-\omega^{-1})^4$?

$\alpha, \beta$ are the roots of the equation $x^2+2x+4=0$. If the point representing $\alpha$ in the Argand diagram lies in the $2^{nd}$ quadrant and $\alpha^{2024}-\beta^{2024}=ik, (i=\sqrt{-1})$,then $k=$