In the linear fractional transformation $T(z)=\frac{az+b}{cz+d}$, if we define $T(-\frac{d}{c})=\infty$, then what is $T(\infty)$?
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It is $a/c$. You can always think of it as $\lim\_{z\to\infty}T(z)$.
$$\lim\_{z\to\infty}T(z)=\lim\_{z\to 0}T(1/z)=\lim\_{z\to 0}\frac{a/z+b}{c/z+d}=\lim\_{z\to 0}\frac{a+bz}{c+dz}=a/c.$$