What is the product of all the values of $(1-i)^{\frac{2}{5}}$?

If $\omega$ is a cube root of unity,then the value of $(1 - \omega + \omega^2)^5 + (1 + \omega - \omega^2)^5$ is:

If $x+\frac{1}{x}=2 \cos \theta$,then for any integer $n$,$x^n+\frac{1}{x^n}=$

If $\omega$ is a complex cube root of unity,then the value of $\frac{a+b \omega+c \omega^2}{c+a \omega+b \omega^2}+\frac{a+b \omega+c \omega^2}{b+c \omega+a \omega^2}$ is:

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

If $(\sqrt{3}+i)^{100}=2^{99}(p+iq)$,then $p$ and $q$ are roots of the equation :