I have the following conformal mapping:
I need to find $\lambda = f(\zeta)$ and its reverse. Zeros on the figure are given, the axis are oriented as usual. The resulting distance between the line and the circle does not matter.
I know how to map the left arrangement to a circle and a line:
$f(\zeta) = -i \frac{\zeta + iA}{\zeta - iA}$
but how do I make the bottom circle transform into a circle with a unit radius?
Unfortunately it's not a homework so you may give an answer as is, should it be easier.