Let $f(z)$ be analytic and nonzero in a region R. Show that $|f(z)|$ has a minimum value in R that occurs on the boundary.
I think you should use the Maximum-Modulus Theorem for the function $1/f(z)$
The Maximum-Modulus Theorem
Let $f(z)$ be analytic and nonzero in a region R. Show that $|f(z)|$ has a minimum value in R that occurs on the boundary.
I think you should use the Maximum-Modulus Theorem for the function $1/f(z)$
The Maximum-Modulus Theorem