If $y = \cos \theta + i\sin \theta$,then the value of $y + \frac{1}{y}$ is

$(27)^{1/3} = $

If $\alpha, \beta$ and $\gamma$ are the roots of $x^3 + 8 = 0$,then the equation whose roots are $\alpha^2, \beta^2$ and $\gamma^2$ is

If $z$ is a complex number such that $z^2+z+1=0$,then $\left(z+\frac{1}{z}\right)^3+\left(z^2+\frac{1}{z^2}\right)^3+\left(z^3+\frac{1}{z^3}\right)^3+\ldots+\left(z^{2020}+\frac{1}{z^{2020}}\right)^3=$

If $\alpha \neq 1$ is any $n^{th}$ root of unity,then $S = 1 + 3\alpha + 5\alpha^2 + \dots$ up to $n$ terms,is equal to

If $z = \left(\frac{\sqrt{3}+i}{2}\right)^5 + \left(\frac{\sqrt{3}-i}{2}\right)^5$, then