$(1+\sqrt{5}+i \sqrt{10-2 \sqrt{5}})^5=$

If $\alpha$ and $\beta$ are imaginary cube roots of unity,then $\alpha^4 + \beta^4 + \frac{1}{\alpha\beta} = $

If $z=x+iy$, $x^2+y^2=1$ and $z_1=ze^{i\theta}$, then $\frac{z_1^{2n}-1}{z_1^{2n}+1}=$

If $1, \omega, \omega^2$ are the cube roots of unity,then $(2-\omega)^2(2-\omega^2)^2(2-\omega^{10})^2(2-\omega^{11})^2=$

Let $A_r = \left(x+\frac{1}{x}\right)^3 \cdot \left(x^2+\frac{1}{x^2}\right)^3 \cdot \left(x^3+\frac{1}{x^3}\right)^3 \cdots \left(x^r+\frac{1}{x^r}\right)^3$. If $x^2+x+1=0$,then $\frac{1}{A_3}+\frac{1}{A_6}+\frac{1}{A_9}+\frac{1}{A_{12}}+\cdots \infty =$

$\sum_{r=1}^{16}\left(\sin \frac{2 r \pi}{17}+i \cos \frac{2 r \pi}{17}\right)=$