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 $z = \frac{\sqrt{3} + i}{2}$,then $\left(z^{101} + i^{103}\right)^{105} = $

$\sqrt{i} = $

If $\alpha$ and $\beta$ are non-real roots of $x^3-x^2-x-2=0$,then $\alpha^{2020}+\beta^{2020}+\alpha^{2020} \cdot \beta^{2020}=$

If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $x^4+x^2+1=0$ such that $\alpha+\beta=-1, \gamma+\delta=1, \alpha^2=\beta$ and $\gamma^2=-\delta$,then $\alpha^{2023}+\beta^{2023}+\gamma^{2022}+\delta^{2022}=$

$\sum_{k=1}^{6} (\sin \frac{2 \pi k}{7} - i \cos \frac{2 \pi k}{7}) = $