9. If $z \in \mathbf{C}, \arg \left(z^{2}-4\right)=\frac{5 \pi}{6}, \arg \left(z^{2}+4\right)=\frac{\pi}{3}$, then the value of $z$ is $\qquad$
Given $B(-4,0), C(4,0)$, then $\angle A B C=\frac{\pi}{3}$, $\angle A C B=\frac{\pi}{6} \Rightarrow \triangle O A B$ is an equilateral triangle.
Thus $A(-2,2 \sqrt{3}) \Rightarrow z^{2}=-2+2 \sqrt{3} \mathrm{i}$.
Let $z=x+y \mathrm{i}(x, y \in \mathbf{R}) \Rightarrow\left\{\begin{array}{l}x^{2}-y^{2}=-2, \\ x y=\sqrt{3}\end{array}\right.$ $\Rightarrow\left\{\begin{array}{l}x=1, \\ y=\sqrt{3}\end{array}\right.$ or $\left\{\begin{array}{l}x=-1, \\ y=-\sqrt{3}\end{array}\right.$. Therefore, $z=1+\sqrt{3} \mathrm{i}$ or $z=-1-\sqrt{3} \mathrm{i}$.