1. If the complex number $z$ satisfies $|z-1|+|z-3-2 \mathrm{i}|=2 \sqrt{2}$, then the minimum value of $|z|$ is
【Analysis】Answer: 1.
Let $z=x+y \mathrm{i}$, then the geometric meaning of $|z-1|+|z-3-2 \mathrm{i}|=2 \sqrt{2}$ is that the sum of the distances from point $P(x, y)$ to points $A(1,0), B(3,2)$ is $2 \sqrt{2}$. Since $|A B|=2 \sqrt{2}$, point $P$ lies on the line segment $A B$, thus: $|O P| \geq 1$. That is, when $z=1$, the minimum value of $|z|$ is $1$.