Suppose that z is a complex number that satisfies $\mid \mathrm{z}-2$$-2\mathrm{i}\mid \le 1$ The maximum value of $|2\mathrm{iz}+4|$ is equal to___________

$|\mathrm{z}-2-2\mathrm{i}|\le 1$
denotes the region inside a circle with center (2, 2) and radius is 1
$\begin{array}{l}|2\mathrm{iz}+4|=\left|2\mathrm{i}\right(\mathrm{z}-2\mathrm{i}\left)\right|\\ =\left|2\mathrm{i}\right||\mathrm{z}-2\mathrm{i}|\\ =2|\mathrm{z}-2\mathrm{i}|\end{array}$
$|\mathrm{z}-2\mathrm{i}|=$ _ distance of z from P(0,2)
Hence, maximum value is 3.