Let $\omega=-\frac{1}{2}+\mathrm{i} \frac{\sqrt{3}}{2}, \mathrm{i}=\sqrt{-1}$, then the value of $\left|\begin{array}{ccc}1 & 1 & 1 \\ 1 & -1-\omega^2 & \omega^2 \\ 1 & \omega^2 & \omega^4\end{array}\right|$ is

Let $Z$ be a complex number such that $|Z|+Z=2+i$ (where $i=\sqrt{-1})$, then $|Z|$ is equal to

If $\mathrm{w}=\frac{-1+i \sqrt{3}}{2}$, where $\mathrm{i}=\sqrt{-1}$, then the value of $\left(3+w+3 w^2\right)^4$ is

If $Z=\frac{-2}{1+\sqrt{3} i}, i=\sqrt{-1}$, then the value of $\arg Z$ is