Complex Numbers

Part of the Undergraduate Texts in Mathematics book series (UTM, volume 0)


One deficiency of the real numbers is that the equation \(x^2 = - 1\ {\rm has\ no\ solution}\ x \in {\rm \mathbf R}\) (Corollary 11.23). In this chapter, we will extend R to overcome this deficiency; the price that we will have to pay is that this extension does not have a useful ordering relation.


Complex Number Geometric Property Real Axis Triangle Inequality Geometric Interpretation 


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Copyright information

© Matthias Beck and Ross Geoghegan 2010

Authors and Affiliations

  1. 1.Department of MathematicsSan Francisco State UniversitySan FranciscoUSA
  2. 2.Department of Mathematical SciencesBinghamton University State University of New YorkBinghamtonUSA

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