Question

If $|z+4|\le 3$ then find the maximum value of $|z+1|$?

Answer 1

$|z+1|=|(z+4)-3|$

$\le |z+4|+\left|3\right|$

$\le 3+3=6$

Note that $z=-7$ satisfies $|z+4|=3$ and $|z+1|=6$.

So the maximum value of $|z+1|$ is $6$