If $1, \omega, \omega^{2}$ are the cube roots of unity,then $(1+\omega)(1+\omega^{2})(1+\omega^{4})(1+\omega^{8})$ is equal to

If $n$ is an integer and $Z = \cos \theta + i \sin \theta$,where $\theta \neq (2n + 1) \frac{\pi}{2}$,then $\frac{1 + Z^{2n}}{1 - Z^{2n}} = $

If the cube root of $1$ is $\omega$,then the value of $(3 + \omega + 3\omega^2)^4$ is

Express the following expression in the form $A + iB$: $(\cos 2\theta + i\sin 2\theta )^{ - 5} (\cos 3\theta - i\sin 3\theta )^6 (\sin \theta - i\cos \theta )^3$.

If $n$ is a positive integer,then $(1 + i)^n + (1 - i)^n$ is equal to

Which of the following is a fourth root of $\frac{1}{2} + \frac{i \sqrt{3}}{2}$?