If $1, \omega, \omega^2$ are the cube roots of unity and $(x+y)(x \omega+y \omega^2)(x \omega^2+y \omega)=f(x, y)$,then $f(2, 3)=$

All the values of $(8i)^{\frac{1}{3}}$ are

The value of $\sum\limits_{r = 1}^8 {\left( {\sin \frac{{2r\pi }}{9} + i\cos \frac{{2r\pi }}{9}} \right)} $ is

Let $\omega (\neq 1)$ be a cubic root of unity. Then the minimum value of the set $\{|a+b\omega+c\omega^2|^2 : a, b, c \text{ are distinct non-zero integers}\}$ equals

If $\theta = \frac{\pi}{6}$,then the $10^{th}$ term of the series $1 + (\cos \theta + i \sin \theta) + (\cos \theta + i \sin \theta)^2 + (\cos \theta + i \sin \theta)^3 + \ldots$ is equal to:

If $z$ is a complex number,then the number of common roots of the equations $z^{1985}+z^{100}+1=0$ and $z^3+2z^2+2z+1=0$ is equal to: