If $1, \omega, \omega^2$ are the three cube roots of unity,then $(3 + \omega^2 + \omega^4)^6 = $

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

Let $\alpha$ and $\beta$ be the roots of $x^2 - \sqrt{2}x + 1 = 0$. Then the value of $\alpha^{50} + \beta^{50}$ is:

If the number of real roots of $x^9-x^5+x^4-1=0$ is $n$,the number of complex roots having argument on the imaginary axis is $m$,and the number of complex roots having argument in the $2^{nd}$ quadrant is $k$,then $m \cdot n \cdot k = $

The product of the four values of $(1+i \sqrt{3})^{3/4}$ is

$A$ complex number $z$ among the following which satisfies $z^3+27 i=0$ is