Editing Maximum modulus principle (section)

== Applications ==
The maximum modulus principle has many uses in complex analysis, and may be used to prove the following:
* The [[fundamental theorem of algebra]].
* [[Schwarz's lemma]], a result which in turn has many generalisations and applications in complex analysis.
* The [[Phragmén–Lindelöf principle]], an extension to unbounded domains.
* The [[Borel–Carathéodory theorem]], which bounds an analytic function in terms of its real part.
* The [[Hadamard three-lines theorem]], a result about the behaviour of bounded holomorphic functions on a line between two other parallel lines in the complex plane.