Question

If $|z+2i|\le 2$, then the least value of $|z-\sqrt{3}+i|$ is :

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

Answer: (A)

$0$

$|z-\sqrt{3}+i|=|(z+2i)-(\sqrt{3}+i)|$
$\Rightarrow |z-\sqrt{3}+i|\ge ||z+2|-|\sqrt{3}+i||$ [$|z_1-z_2|\ge ||z_1|-|z_2||]$

$\ge 2-\sqrt{3+1}=2-2=0$

Hence least value of $|z-\sqrt{3}+i|$ is $0$