Complex Numbers

  • Authors
  • Walter Ledermann

Part of the Library of Mathematics book series (LIMA)

Table of contents

  1. Front Matter
    Pages i-vi
  2. Walter Ledermann
    Pages 1-13
  3. Walter Ledermann
    Pages 14-32
  4. Walter Ledermann
    Pages 33-42
  5. Walter Ledermann
    Pages 43-61
  6. Back Matter
    Pages 62-64

About this book

Introduction

THE purpose of this book is to present a straightforward introduction to complex numbers and their properties. Complex numbers, like other kinds of numbers, are essen­ tially objects with which to perform calculations according to certain rules, and when this principle is borne in mind, the nature of complex numbers is no more mysterious than that of the more familiar types of numbers. This formal approach has recently been recommended in a Reportt prepared for the Mathematical Association. We believe that it has distinct advantages in teaching and that it is more in line with modern algebraical ideas than the alternative geometrical or kinematical definitions of ..; - 1 that used to be proposed. On the other hand, an elementary textbook is clearly not the place to enter into a full discussion of such questions as logical consistency, which would have to be included in a rigorous axiomatic treatment. However, the steps that had to be omitted (with due warning) can easily be filled in by the methods of abstract algebra, which do not conflict with the 'naive' attitude adopted here. I should like to thank my friend and colleague Dr. J. A. Green for a number of valuable suggestions, especially in connection with the chapter on convergence, which is a sequel to his volume Sequences and Series in this Library.

Keywords

Calc Calculation Mathematica Unity Volume algebra complex number convergence form function functions logarithm object presentation types

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-7730-6
  • Copyright Information Springer-Verlag US 1960
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-7100-8634-1
  • Online ISBN 978-1-4684-7730-6
  • About this book