Question

If $|z+4|\le 3,$ then the maximum value of $|z+1|$ is

Answer 1

Given,
$|z+4|\le 3\dots \left(i\right)$
Now,
$|z+1|=|z+4-3|$

We know that,
$|z_1-z_2|\le |z_1|+|z_2|\therefore |z+4-3|\le |z+4|+3\dots \left(ii\right)$

From $\left(i\right)$ and $\left(ii\right),$ we get
$\Rightarrow |z+1|\le 3+3$
$\Rightarrow |z+1|\le 6$

Hence, maximum value of $|z+1|$ is $6.$