A Möbius transform is a complex-valued function of the form
$$
f(z)=\frac{a z+b}{c z+d}
$$
(a, $b, c$, and $d$ are complex numbers).
1. Find $a, b, c$, and $d$, such that
$$
\begin{array}{ll}
f(0) & =1, \\
f(1) & =1+i, \\
f(1+i) & =\infty
\end{array}
$$
2. Illustrate $f$ using ComplexParametricMap [] by choosing suitable sets of lines that show the essential features of $f$. Identify the values $f(0)$ and $f(\infty)$ in the diagrams.