Question

The greatest value of $|z+1|$ if $|z+4|\le 3$ is

• A. 4
• B. 5
• C. 6
• D. None of these

Answer 1

The correct option is C 6

We have,

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

By using $|z_1+z_2|\le |z_1|+|z_2|$ we have

$|(z+4)+(-3)|\le |z+4|+|-3|=|z+4|+3$

$|(z+4)+(-3)|\le 3+3=6(\because |z+4|\le 3)$

Hence, the greatest value of $|z+1|$ is $6$