If $\omega$ is a non-real cube root of unity and $x = \omega^2 - \omega - 3$,then the value of $x^4 + 6x^3 + 10x^2 - 12x - 19$ is

If $\left(\frac{1+i}{1-i}\right)^{\frac{m}{2}}=\left(\frac{1+i}{i-1}\right)^{\frac{n}{3}}=1$ where $m, n \in N$,then the greatest common divisor of the least values of $m$ and $n$ is:

If $Z = r(\cos \theta + i \sin \theta), (\theta \neq -\pi / 2)$ is a solution of $x^3 = i$,then $r^9(\cos \theta + i \sin \theta)^9 = $

If $1, \omega, \omega^2$ are the cube roots of unity,$n \in \mathbb{N}$ and $n > 2$,then the least value of $n$ such that $1+\omega$ is a root of $x^n-x=0$ is

The value of $\frac{(\cos \theta + i \sin \theta)^4}{(\sin \theta + i \cos \theta)^5}$ is equal to,where $i = \sqrt{-1}$:

If $z$ is a non-real root of $x^7=1$,then $1+3z+5z^2+7z^3+9z^4+11z^5+13z^6=$