If $\alpha$ and $\beta$ are the roots of the equation $x^2-x+1=0$,then $\alpha^{2009}+\beta^{2009}$ is equal to

If $n$ is a positive integer and $\omega \neq 1$ is a cube root of unity,the number of possible values of $\left|e^{\sum_{k=0}^n {^nC_k} \omega^k}\right|$ is

Let $\omega$ be an imaginary cube root of unity. Then the value of $2(\omega + 1)(\omega^2 + 1) + 3(2\omega + 1)(2\omega^2 + 1) + \dots + (n + 1)(n\omega + 1)(n\omega^2 + 1)$ is

If $\omega$ is an imaginary cube root of unity,then the value of $(1-\omega+\omega^{2}) \cdot(1-\omega^{2}+\omega^{4}) \cdot(1-\omega^{4}+\omega^{8}) \cdot \ldots$ ($2n$ factors) is

The sum of the products of the non-conjugate roots of $i^{1/4}$ taken two at a time is

The value of $(1 - \omega + \omega^2)(1 - \omega^2 + \omega)^6$,where $\omega, \omega^2$ are the complex cube roots of unity.