One of the cube roots of unity is

If $\omega$ is a complex cube root of unity,then $(x+1)(x+\omega)(x-\omega-1)$ is equal to

If $\omega$ is a complex cube root of unity,then $\omega^{\left(\frac{1}{3}+\frac{2}{9}+\frac{4}{27}+\ldots \infty\right)}+\omega^{\left(\frac{1}{2}+\frac{3}{8}+\frac{9}{32}+\ldots \infty\right)}$ is equal to

If $\alpha$ and $\beta$ are the complex cube roots of unity,then $\alpha^3+\beta^3+\alpha^{-2} \times \beta^{-2}$ is equal to

The product of all the values of $(\sqrt{3}-i)^{\frac{3}{7}}$ is

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 $f(2, 3)=$