Question

If $z$ is any complex number such that $|z-5|\le 10$, then find the greatest value of $\left|z\right|$

Answer 1

Given that, $|z-5|\le 10$

$|z|=|z+5-5|$

$=|z-5+5|$

$\le |z-5|+|5|$

$\le 10+5=15$

$\therefore$ greater value $=15$