(5) Given a complex number $z$ satisfying $|z|=1$, let $u=z^{4}-z^{3}-3 \mathrm{i} z^{2}-z+1$, find $\max |u|$ and $\min |u|$.
(Answer: When $z=1$ or $-\frac{1}{2} \pm \frac{\sqrt{3}}{2} \mathrm{i}$, $\min |u|=3$; When $z=-1$, $\max |u|=5$)