Complex Numbers
THE purpose of this book is to prescnt 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 a:cording to certain rules, and when
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COMPLEX NUMBERS
LIBRARY OF MATHEMATICS edited by WALTER LEDERMANN D.Sc., Ph.D., F.R.S.Ed., Professor of Mathematics, University of Sussex
Linear Equations Sequences and Series Differential Calculus Elementary Differential Equations and Operators Partial Derivatives Complex Numbers Principles of Dynamics Electrical and Mechanical Oscillations Vibrating Systems Vibrating Strings Fourier Series Solutions of Laplace's Equation Solid Geometry Numerical Approximation Integral Calculus Sets and Groups Differential Geometry Probability Theory Multiple Integrals Fourier and Laplace Transforms Introduction to Abstract Algebra Functions of a Complex Variable, 2 Vols Linear Programming Sets and Numbers Calculus of Variations
P.M.Cohn J. A. Green P. J. Hilton G. E. H. Reuter P. J. Hilton W. Ledermann M. B. Glauert D. S. Jones R. F. Chisnell D. R. Bland I. N. Sneddon D. R. Bland P. M. Cohn B. R. Morton W. Ledermann J. A. Green K. L. Wardle A. M. Arthurs W. Ledermann P. D. Robinson C. R. J. Clapham D. O. Tall Kathleen Trustrum S. Swierkoswki A. M. Arthurs
COMPLEX NUMBERS BY
WALTER LEDERMANN
Routledge & Kegan Paul LONDON AND HENLEY
First published I960 in Great Britain by Routledge &J Kegan Paul Limited 39 Store Street London WeIE TDD and Broadway House, Newtown Road Henley-on-Thames, Oxon RGc; IEN
© Walter Ledermann I960,
I96a
Second impression (with some corrections) I96a Reprinted I964, I96S, I967, I97I and I976
No part of this book may be reproduced in any form without permission from the publisher, except fOT the quotation of brief passages in criticism ISBN 978-0-7100-4345-0
001 10.1007/978-94-011-6570-9
ISBN 978-94-011-6570-9
(eBook)
Preface purpose of this book is to prescnt a straightforward introduction to complex numbers and their properties. Complex numbers, like other kinds of numbers, are essentially objects with which to perform calculations a:cording 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 v - 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. THE
WALTER LEDERMANN
t The Teaching of Algebra in Sixth Forms, C
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