If $\alpha$ and $\beta$ are the roots of the equation $x^2 - 2x + 2 = 0$,then the least value of $n$ for $(\frac{\alpha}{\beta})^n = 1$ is

If $z = \frac{\sqrt{3} + i}{2}$,then the value of $z^{69}$ is

If $x^{2}+x+1=0$, then the value of $(x+\frac{1}{x})^{4}+(x^{2}+\frac{1}{x^{2}})^{4}+(x^{3}+\frac{1}{x^{3}})^{4}+\dots+(x^{25}+\frac{1}{x^{25}})^{4}$ is:

If $\omega$ is a non-real cube root of unity,then the value of $\cos \left[ \left\{ (1-\omega)(1-\omega^2) + (2-\omega)(2-\omega^2) + \dots + (2017-\omega)(2017-\omega^2) \right\} \cdot \frac{\pi}{2017} \right]$ is -

If $\omega$ is the complex cube root of unity and $\left(\frac{a+b \omega+c \omega^2}{c+a \omega+b \omega^2}\right)^k+\left(\frac{a+b \omega+c \omega^2}{b+a \omega^2+c \omega}\right)^l=2$,then $2k+l$ is always

If $\omega$ is a complex cube root of unity,then $(x+1)(x+\omega)(x-\omega-1)$ is equal to