Question

For any complex number $z$, the minimum value of $|z|+|z-3i|$ is

Answer 1

We have,
$|3i|=|z+(3i-z)|\le |z|+|3i-z|$
$\Rightarrow 3\le |z|+|z-3i|$
Thus, minimum value of $|z|+|z-3i|$ is $3$.