Briefly, the maximum modulus principle states that if \(f\) is analytic and not constant in a domain \(A\) then \(|f(z)|\) has no relative maximum in \(A\) and the absolute maximum of \(|f|\) occurs o...Briefly, the maximum modulus principle states that if \(f\) is analytic and not constant in a domain \(A\) then \(|f(z)|\) has no relative maximum in \(A\) and the absolute maximum of \(|f|\) occurs on the boundary of \(A\). If \(A\) is bounded and connected, and \(f\) is continuous on \(A\) and its boundary, then either \(f\) is constant or the absolute maximum of \(|f|\) occurs only on the boundary of \(A\).
