Question

For any complex number z, find the minimum value of $\left|z\right|+|z-2i|.$

Answer 1

We have, for $z\in C$
$\left|2i\right|=|z+(2i-z\left)\right|\le \left|z\right|+|2i-z|$
$\Rightarrow 2\le \left|z\right|+|z-2i|$
Thus, minimum value of $\left|z\right|+|z-2i|$ is 2.
Ans: 2