1. If the complex number $z$ satisfies
$$
|z-1|+|z-3-2 i|=2 \sqrt{2} \text {, }
$$

then the minimum value of $|z|$ is $\qquad$ .
,- 1.1 .
Let $A(1,0), B(3,2),|A B|=2 \sqrt{2}$.
Then the locus of point $z$ is the line segment $A B$.
Therefore, $|z|_{\text {min }}$ is the distance from the origin $O$ to $A$, i.e., $|z|_{\text {min }}=|O A|=1$.