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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.

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Cite

@article{arxiv.1304.4261,
  title  = {A short proof of d'Alemberts theorem},
  author = {Tord Sjödin},
  journal= {arXiv preprint arXiv:1304.4261},
  year   = {2013}
}

Comments

3 pages

R2 v1 2026-06-22T00:00:06.771Z