7. Given a complex number $z$ satisfying $|z|=1$. Then the maximum value of $\left|z^{3}-3 z-2\right|$ is $\qquad$ .

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$7.3 \sqrt{3}$.
Let $z=a+b$ i. Then $a^{2}+b^{2}=1$.
Thus $\left|z^{3}-3 z-2\right|=|z+1|^{2}|z-2|$
$=2(a+1) \sqrt{5-4 a}$
$=\sqrt{(2 a+2)(2 a+2)(5-4 a)} \leqslant 3 \sqrt{3}$.
When $a=\frac{1}{2}, b= \pm \frac{\sqrt{2}}{2}$, the equality holds.