Question

If $z$ be a complex number satisfying $|z-4+8i|=4,$ then the least and the greatest value of $|z+2|$ are respectively (where $i=\sqrt{-1}$ )

• A. $7$ and $16$
• B. $8$ and $17$
• C. $6$ and $14$
• D. $5$ and $13$

Answer 1

Answer: (C)

$|z+2|=|z+2-4+8i+4-8i|$
$|z+2|=|z-4+8i+6-8i|$
$\left|z+2\right|\le |z-4+8i|+|6-8i|$
$\le 4+10=14$
$|z+2|=|z+2-4+8i+4-8i|$
$\ge |z-4+8i|-|6-8i|$
$\ge \left|4-10\right|=6$