find a conformal map, which maps the exterior of circles $B(-\frac{1}{2},\frac{1}{2})$ and $B(\frac{1}{2}, \frac{1}{2})$, in addition excluded segment $[-2i,0]$, into the upper half plane.
My thoughts: I wish I can map each of these circles into a quadrant, map the segment into the eel axis and take completion, but I don't know how to do specifically. Thanks for any help.
Hint: The function $f(z) = 1/(z-1/2)$ is a conformal map of $\mathbb C \setminus \{|z-1/2| \le 1/2\}$ into $D(0,2).$