8. Given a complex number $z$ satisfying $|z|=1$. Then
$$
f(z)=\left|z^{5}+\bar{z}^{3}+6 z\right|-2\left|z^{4}+1\right|
$$

the minimum value of $f(z)$ is $\qquad$
8. 3 .

Let $x=z^{2}+\bar{z}^{2} \in[-2,2]$. Then
$$
\begin{array}{l}
f(z)=\left|x^{2}+4\right|-2|x| \\
=(|x|-1)^{2}+3 \in[3,4] .
\end{array}
$$