Throughout this part, $f$ denotes a function that expands in a power series on $D(0,R)$, i.e.,
$$\forall (x,y) \in D(0,R), \quad f(x,y) = \sum_{n=0}^{+\infty} a_n (x + \mathrm{i} y)^n$$
Show that if $|f|$ attains a maximum at 0, then $f$ is constant on $D(0,R)$.