Question

If $z$ is a complex number then
the minimum value of $|z|+|z-1|+|2z-3|$ is

Answer 1

$|z|+|z-1|+|2z-3|$
$=z|+|z-1|+|3-2z|\ge |z+z-1+3-2z|$
$\Rightarrow |z|+|z-1|+|3-2z|\ge 2$