Hint for Q 3 p. 97 Ahlfors continued:

The problem asks you to conformally map the plane with a half-circle arc cut out, to the complement of the unit disk.

Map F_1: Find this LFT that maps {-1,i,1} to {-1,0,1} in that order, and thus the arc segment given to the line segment [-1,1]:

f(z) = [(1+i)z + (1-i)]/[(1-i)z + (1+i)]