I have the following two circles in the complex plane, $z = x + iy$, which bound a region, $R$. The equations for the circles and a sketch of the region is given as follows: $$ x^2 + (y-1)^2 = 1\\ x^2 + (y-2)^2 = 4 $$
https://i.stack.imgur.com/n7iVd.png
What I now want to do is map the region bounded by these two circles and sketch some new region, $W$, defined as follows: $$ W = \{ w = e^{4 \pi/z} \hspace{0.3mm} : \hspace{0.5mm} z \in R \}$$
And I am a bit lost in all honesty. Any help or push in the right direction would be greatly appreciated.