Liouville's Boundedness Theorem

A bounded Entire Function in the Complex Plane $\Bbb{C}$ is constant. The Fundamental Theorem of Algebra follows as a simple corollary.

See also Complex Plane, Entire Function, Fundamental Theorem of Algebra

References

Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 381-382, 1953.