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Disciplina: Cálculo Diferencial e Integral
MATEMÁTICA PURA
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Teorema Fundamental da Álgebra
Em Matemática Pura, o Teorema Fundamental da Álgebra afirma que qualquer Polinómio p(z) com Coeficientes Complexos de Uma Variável e de Grau n ≥ 1 tem alguma raiz complexa. Por outras palavras, o Corpo dos Números Complexos é Algebricamente Fechado e, portanto, tal como com qualquer outro Corpo Algebricamente Fechado, a equação P(z)=0 tem n Soluções não necessariamente Distintas.
![](https://static.wixstatic.com/media/26a617_d151ab76b29b4a69bce975d8b04963c0.png/v1/fill/w_59,h_50,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/26a617_d151ab76b29b4a69bce975d8b04963c0.png)
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Bibliografia
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A.-L. Cauchy, Cours d'Analyse de l'École Royale Polytechnique, 1ère partie: Analyse Algébrique, 1992, Éditions Jacques Gabay.
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B. Fine e G. Rosenberger, The Fundamental Theorem of Algebra, 1997, Springer-Verlag.
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C. F. Gauss, «New Proof of the Theorem That Every Algebraic Rational Integral Function In One Variable can be Resolved into Real Factors of the First or the Second Degree», 1799
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C. Gilain, «Sur l'histoire du théorème fondamental de l'algèbre: théorie des équations et calcul intégral», Archive for History of Exact Sciences, 42 (1991), 91–136
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E. Netto e R. Le Vavasseur, «Les fonctions rationnelles §80–88: Le théorème fondamental», em Encyclopédie des Sciences Mathématiques Pures et Appliquées, tome I, vol. 2, 1992, Éditions Jacques Gabay.
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R. Remmert, «The Fundamental Theorem of Algebra», em Numbers, 1991, Springer-Verlag.
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D. E. Smith, «A Source Book in Mathematics», 1959, Dover Publications.
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F. Smithies, «A forgotten paper on the fundamental theorem of algebra», Notes & Records of the Royal Society.
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M. Spivak, Calculus, 1994, Publish or Perish.
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B. L. van der Waerden, Algebra I, 1991, Springer-Verlag.
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C. Baltus, «D’Alembert proof of the fundamental theorem of algebra», Historia Mathematica 31 (2004) 414-428
Artigos Relacionados
1) Teorema Fundamental da Álgebra. Arquivo no Formato ".PDF" - Tamanho do Arquivo = 722kb.
2) Teorema Fundamental da Álgebra. Arquivo no Formato ".PDF" - Tamanho do Arquivo = 87,2kb.
Uma Demonstração do Teorema Fundamental da Álgebra
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