If $z = \frac{\sqrt{3}}{2} + \frac{i}{2}$, where $i = \sqrt{-1}$, then $(z^{201} - i)^{8}$ is equal to:

If the complex number $a$ is such that $|a|=1$ and $\arg (a)=\theta$,then the roots of the equation $\left(\frac{1+i z}{1-i z}\right)^4=a$ are $z=$

If $\omega$ is a complex cube root of unity,then $(1 + \omega)(1 + \omega^2)(1 + \omega^4)(1 + \omega^8) \dots$ to $2n$ factors is equal to:

If $\alpha, \beta$ are the roots of the equation $x^2+x+1=0$,then $(\alpha+\beta)^2+(\alpha^2+\beta^2)^2+(\alpha^3+\beta^3)^2+\ldots+(\alpha^{12}+\beta^{12})^2=$

If $(1 + i\sqrt{3})^9 = a + ib$,then $b$ is equal to

If $n$ is a positive integer not a multiple of $3$,then $1 + \omega^n + \omega^{2n} = $