If $1, \omega, \omega^2$ are the cube roots of unity,then $(2-\omega)^2(2-\omega^2)^2(2-\omega^{10})^2(2-\omega^{11})^2=$

In the Argand plane,no value of $\sqrt[3]{1-i \sqrt{3}}$ lies in which quadrant?

If $z^{2} + z + 1 = 0$,$z \in \mathbb{C}$,then $\left| \sum_{n=1}^{15} \left( z^{n} + (-1)^{n} \frac{1}{z^{n}} \right)^{2} \right|$ is equal to

If $1, \omega$ and $\omega^2$ are the cube roots of unity,then $(a+b+c)(a+b \omega+c \omega^2)(a+b \omega^2+c \omega) = $

If $Z \neq 0$ is a complex number such that $Z^2 + Z|Z| + |Z|^2 = 0$,then $Z$ is in the set (Here $\omega$ is a complex cube root of unity).

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