grandes-ecoles 2018 Q36

grandes-ecoles · France · centrale-maths2__official Complex numbers 2 Properties of Analytic/Entire Functions

Let $f$ be a function that expands as a power series on $D(0,R)$. Show that if $|f|$ attains a maximum at 0, then $f$ is constant on $D(0,R)$.

Let $f$ be a function that expands as a power series on $D(0,R)$. Show that if $|f|$ attains a maximum at 0, then $f$ is constant on $D(0,R)$.