Question

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

• A. $3$
• B. $5$
• C. $1$
• D. $4$

Answer 1

The correct option is D $4$

$|z+2i|\le 2$ represents the area inside the circle with centre $A(0,-2)$ and radius 2 in the argand plane.

The required greatest value is the distance of point z on circle from the point $B(\sqrt{3},-1)$

Point $B(\sqrt{3},-1)$ lies on circle.

So the farthest point $C$ on the circle from given point $B$ is on the other end of the diameter.

The distance between $(\sqrt{3},-1)$ and the centre is 2. The farthest point $C$ on the circle would be at a distance of $2+2=4$ units from $B(\sqrt{3},-1)$

Hence, option D is correct