9. The complex number $z=\cos \theta-\mathrm{i}(\sin \theta-1), \theta \in\left(\frac{\pi}{2}, \pi\right), \omega=z^{2}-2 \mathrm{i} z$, then the trajectory of the point corresponding to $\omega$ in the complex plane is . $\qquad$
9. A semicircle (excluding endpoints) $\omega=[\cos \theta-\mathrm{i}(\sin \theta-1)] \times[\cos \theta-\mathrm{i}(\sin \theta+1)]$
$=\cos ^{2} \theta-\left(\sin ^{2} \theta-1\right)-\mathrm{i} \cdot 2 \cos \theta \cdot \sin \theta=\cos 2 \theta+1-\mathrm{i} \sin 2 \theta$
$2 \theta \in(\pi, 2 \pi)$, so $\cos 2 \theta+1>0,-\sin 2 \theta>0$
Let $\cos 2 \theta+1=x,-\sin 2 \theta=y$, so $(x-1)^{2}+y^{2}=1, x>0, y>0$