If the complex number $z=x+i y$, where $i=\sqrt{-1}$, satisfies the condition $|z+1|=1$, then $z$ lies on

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

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