I have run into some confusion while reading Newman Bak's Complex Analysis.
The text states that if we wish to determine a comformal mapping $h$ of the upper half-plane onto the unit disk, assuming that $h$ is bilinear and $h(\alpha)=0$ for fixed $\alpha$ with $Im(\alpha)>0$, then "since the real axis is mapped into the unit circle, it follows by the Schwartz Reflection Principle that $h(\bar\alpha)=\infty.$"
How exactly does the Schwartz Reflection Principle imply that $h(\bar\alpha)=\infty$? I can see that since $h$ is an automorphism of the Riemann Sphere, $h(\alpha)$ is contained in the interior of the sphere so that $h(\bar\alpha)$ must be contained in the exterior. However, I don't see why $h(\bar\alpha)=\infty.$