If $1, \alpha_1, \alpha_2, \alpha_3, \alpha_4$ are the roots of $z^5-1=0$ and $\omega$ is a cube root of unity,then $(\omega-1)(\omega-\alpha_1)(\omega-\alpha_2)(\omega-\alpha_3)(\omega-\alpha_4)+\omega$ is equal to

$\frac{(\cos \alpha + i\sin \alpha )^4}{(\sin \beta + i\cos \beta )^5} = $

One of the roots of the equation $(x+1)^4 + 81 = 0$ is

${\left( \frac{1 + \cos \phi + i\sin \phi }{1 + \cos \phi - i\sin \phi } \right)^n} = $

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 $\frac{\alpha-h}{\beta-h}+\frac{\beta-h}{\gamma-h}+\frac{\gamma-h}{\alpha-h}=$

$(-\sqrt{3} + i)^{53}$,where $i^2 = -1$,is equal to: