A short proof of d'Alemberts theorem
History and Overview
2013-04-17 v1
Abstract
A classical theorem of d'Alembert states that if a polynomial P(x) with real coefficients has a non-real root x=a+ib, then it also has a root x=a-ib. We give a short and elementary inductive proof that avoids any properties of the complex conjugation operator.
Cite
@article{arxiv.1304.4261,
title = {A short proof of d'Alemberts theorem},
author = {Tord Sjödin},
journal= {arXiv preprint arXiv:1304.4261},
year = {2013}
}
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3 pages