# Solve the following

Question:

If $|z+4| \leq 3$, then find the greatest and least values of $|z+1|$.

Solution:

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

$\leq|z+4|+|-3|$

$\leq 3+3$

$=6$

Also,

$|z+1| \geq 0$

Thus, $0 \leq|z+1| \leq 6$.

Hence, the greatest and least values of $|z+1|$ is 6 and 0 .