Complex Numbers

$A\left(z_1=2+2 i\right), B\left(z_2\right), C\left(z_3\right)$ are three points on the Argand plane satisfying $\left|z_k-2 i\right|=2,(k=1,2,3)$. If $\triangle A B C$ encloses the maximum area, then the sum of the imaginary parts of $z_2$ and $z_3$ is