Complex Numbers

  • Antonio Caminha Muniz Neto
Part of the Problem Books in Mathematics book series (PBM)


It is an obvious fact that the set of reals is too small to provide a complete description of the set of roots of polynomial functions; for instance, the function xx2 + 1, with \(x\in \mathbb R\), does not have any real root. Historically, the search for such roots strongly motivated the birth of complex numbers and the flowering of complex function theory. In this respect, a major first crowning was the proof, by Gauss, of the famous Fundamental Theorem of Algebra, which asserts that every polynomial function with complex coefficients has a complex root.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Antonio Caminha Muniz Neto
    • 1
  1. 1.Universidade Federal do CearáFortalezaBrazil

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