Question

If $|z+4|\le 3$, then the greatest and the least value of $|z+1|$ are

• A. $-1,6$
• B. $6,0$
• C. $6,3$
• D. None of these

Answer 1

Answer: (B)

$6,0$

$|z+4|\le 3\Rightarrow -3\le z+4\le 3$
$\Rightarrow -6\le z+1\le 0$
$\Rightarrow 0\le -(z+1)\le 6$
$\Rightarrow 0\le |z+1|\le 6$
Hence, the greatest and least values are $6$ and $0$.