Question

If z is a complex number such that $|z-2-2i|\le 1,$ then the maximum value of $|2iz+4|$ is equal to

• A. $6$
• B. $5$
• C. $4$
• D. $3$

Answer 1

The correct option is D $3$

$|z-2-2i|\le 1$ is the region inside the circle with center at $(2,2)$ and radius $1$
$|2iz+4|=2|z-2i|$ is the distance of $(0,2)$ from the circle
So, the maximum distance of $(0,2)$ from the circle is $3$ as can be seen from the figure .
Hence, option A is correct