If $\omega = \frac{-1 + \sqrt{3}i}{2}$,then $(3 + \omega + 3\omega^2)^4 = $

If $x = a + b$,$y = a\alpha + b\beta$,and $z = a\beta + b\alpha$,where $\alpha$ and $\beta$ are complex cube roots of unity,then $xyz$ =

If $x_n = \cos \frac{\pi}{2^n} + i \sin \frac{\pi}{2^n}$,then $\prod_{n=1}^{\infty} x_n$ is equal to

One of the values of $(\sqrt{3}-i)^{\frac{1}{6}}$ is

The number of distinct solutions of the equation $x^{11}-x^7+x^4-1=0$ is

Let $\alpha = \frac{-1 + i \sqrt{3}}{2}$. If $a = (1 + \alpha) \sum_{k=0}^{100} \alpha^{2k}$ and $b = \sum_{k=0}^{100} \alpha^{3k}$,then $a$ and $b$ are the roots of the quadratic equation: