Question:
Suppose that $f(z)$ is a conformal mapping of $\{\mathrm{Im}(z)>0\}$ onto the unit square $$\{0<\mathrm{Re}(z)<1,\;0<\mathrm{Im}(z)<1\}$$ such that the boundary points $0$, $1$, $\infty$ correspond to $0$, $1$, $1+i$ respectively.
a) Which point $x$ on the real axis corresponds to the vertical $i$?
b) Prove that $f^{-1}$ has an analytic continuation to a meromorphic function $F$.
Thanks.
I think it should be related to Schwartz Christoffel.