Question

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

• A. $3$
• B. $4$
• C. $8$
• D. $12$

Answer 1

The correct option is C $8$

We are given that $|z-1|\le 3$

We need to find the maximum value of $|z+4|$

$|z+4|=|z+5-1|=|z-1+5|$

Now by the property of "triangle inequality" we have,

$|z-1+5|\le |z-1|+5$

$\Rightarrow |z+4|\le 3+5=8$
Hence, option C is correct.