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Introduction

  • Eberhard FreitagEmail author
  • Rolf Busam
Chapter
  • 7.8k Downloads
Part of the Universitext book series (UTX)
The complex numbers have their historical origin in the 16th century when they were created during attempts to solve algebraic equations. G. CARDANO (1545) has already introduced formal expressions as for instance \(5 \pm \sqrt{-15}\), in order to express solutions of quadratic and cubic equations. Around 1560 R. BOMBELLI computed systematically using such expressions and found 4 as a solution of the equation \(x^3 = 15x + 4\) in the disguised form
$$4 = \sqrt[3]{2 + \sqrt{-121}} + \sqrt[3]{2 - \sqrt{-121}}$$
Also in the work of G.W. LEIBNIZ (1675) one can find equations of this kind, e.g.
$$\sqrt{1 + \sqrt{-3}} + \sqrt{1 - \sqrt{-3}} = \sqrt{6}.$$
In the year 1777 L. EULER introduced the notation \({\rm{i}} = \sqrt{-1}\) for the imaginary unit.

Keywords

Modular Form Elliptic Function Dirichlet Series Modular Function Real Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Universität HeidelbergInst. MathematikGermany

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