If $\left(\frac{\sqrt{3}+i}{\sqrt{3}-i}\right)^m=1$ and $2022 < m < 2029$,then $m=$

Let $\alpha$ and $\beta$ be the roots of $x^2 + \omega x + \omega^2 = 0$,where $\omega$ is an imaginary cube root of unity. If $z = \alpha^9 + i\beta^9$,then the value of $|z|$ is:

Two values of $(-8-8 \sqrt{3} i)^{1/4}$ are

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 $\omega_0, \omega_1, \ldots, \omega_{n-1}$ are the $n$-th roots of unity,then $(1+2 \omega_0)(1+2 \omega_1)(1+2 \omega_2) \ldots (1+2 \omega_{n-1})=$

If $\frac{1}{x} + x = 2\cos \theta,$ then ${x^n} + \frac{1}{{{x^n}}}$ is equal to