Question

Suppose that $z$ is a complex number that satisfies $|z-2-2i|\le 1$. The Maximum value of $|2z-4i|$ is equal to ____.

Answer 1

Given that $|z-2-2i|\le 1$
Now, $|2z-4i|=2|z-2-2i+2|\le 2(|z-2-2i|+\left|2\right|)\le 2(1+2)$
Therefore, $|2z-4i|\le 6$
Ans: 6