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Complex Numbers from A to Z

Complex Numbers from A to    Z Book
Author : Titu Andreescu,Dorin Andrica
Publisher : Springer Science & Business Media
Release : 2007-10-08
ISBN : 0817644490
Language : En, Es, Fr & De

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Book Description :

* Learn how complex numbers may be used to solve algebraic equations, as well as their geometric interpretation * Theoretical aspects are augmented with rich exercises and problems at various levels of difficulty * A special feature is a selection of outstanding Olympiad problems solved by employing the methods presented * May serve as an engaging supplemental text for an introductory undergrad course on complex numbers or number theory

Complex Numbers

Complex Numbers Book
Author : Walter Ledermann
Publisher : Springer Science & Business Media
Release : 2013-03-14
ISBN : 940116570X
Language : En, Es, Fr & De

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Book Description :

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 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.

Pure mathematics

Pure mathematics Book
Author : Anthony Nicolaides
Publisher : PASS PUBLICATIONS
Release : 2007
ISBN : 1872684920
Language : En, Es, Fr & De

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Book Description :

Complex Numbers and Vectors

Complex Numbers and Vectors Book
Author : Les Evans
Publisher : Aust Council for Ed Research
Release : 2006
ISBN : 0864315325
Language : En, Es, Fr & De

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Book Description :

Complex Numbers and Vectors draws on the power of intrigue and uses appealing applications from navigation, global positioning systems, earthquakes, circus acts and stories from mathematical history to explain the mathematics of vectors and the discoveries of complex numbers. The text includes historical and background material, discussion of key concepts, skills and processes, commentary on teaching and learning approaches, comprehensive illustrative examples with related tables, graphs and diagrams throughout, references for each chapter (text and web-based), student activities and sample solution notes, and an extensive bibliography.

Complex Numbers

Complex Numbers Book
Author : Glen Prideaux
Publisher : Lulu.com
Release : 2016-09-27
ISBN : 1365424898
Language : En, Es, Fr & De

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Book Description :

A set of well designed, graded practice problems for secondary students covering aspects of complex numbers including modulus, argument, conjugates, arithmetic, the complex plane, roots of quadratic equations, the factor and remainder theorems applied to polynomial functions, Cartesian and polar representations, De Moivre's theorem, complex roots, and Euler's theorem. Solutions are provided for odd-numbered questions.

Complex Numbers Made Simple

Complex Numbers Made Simple Book
Author : Verity Carr
Publisher : Newnes
Release : 1996
ISBN : 0750625597
Language : En, Es, Fr & De

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Book Description :

Complex Numbers lie at the heart of most technical and scientific subjects. This book can be used to teach complex numbers as a course text,a revision or remedial guide, or as a self-teaching work. The author has designed the book to be a flexible learning tool, suitable for A-Level students as well as other students in higher and further education whose courses include a substantial maths component (e.g. BTEC or GNVQ science and engineering courses). Verity Carr has accumulated nearly thirty years of experience teaching mathematics at all levels and has a rare gift for making mathematics simple and enjoyable. At Brooklands College, she has taken a leading role in the development of a highly successful Mathematics Workshop. This series of Made Simple Maths books widens her audience but continues to provide the kind of straightforward and logical approach she has developed over her years of teaching.

Complex Numbers and Geometry

Complex Numbers and Geometry Book
Author : Liang-shin Hahn
Publisher : Cambridge University Press
Release : 1994
ISBN : 9780883855102
Language : En, Es, Fr & De

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Book Description :

This book demonstrates how complex numbers and geometry can be blended together to give easy proofs of many theorems in plane geometry.

Geometry of Complex Numbers

Geometry of Complex Numbers Book
Author : Hans Schwerdtfeger
Publisher : Courier Corporation
Release : 2012-05-23
ISBN : 0486135861
Language : En, Es, Fr & De

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Book Description :

Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.

Calculus with Complex Numbers

Calculus with Complex Numbers Book
Author : John B. Reade
Publisher : CRC Press
Release : 2003-03-13
ISBN : 9780415308465
Language : En, Es, Fr & De

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Book Description :

This practical treatment explains the applications complex calculus without requiring the rigor of a real analysis background. The author explores algebraic and geometric aspects of complex numbers, differentiation, contour integration, finite and infinite real integrals, summation of series, and the fundamental theorem of algebra. The Residue Theorem for evaluating complex integrals is presented in a straightforward way, laying the groundwork for further study. A working knowledge of real calculus and familiarity with complex numbers is assumed. This book is useful for graduate students in calculus and undergraduate students of applied mathematics, physical science, and engineering.

Complex Numbers

Complex Numbers Book
Author : W. Bolton
Publisher : Longman Group United Kingdom
Release : 1995
ISBN : 9780582237414
Language : En, Es, Fr & De

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Book Description :

This book is part of a series designed to provide engineering students in colleges and universities with a mathematical toolkit, each book including the mathematics in an engineering context. Worked examples and problems with answers are included.

Maths for Chemists Power series complex numbers and linear algebra

Maths for Chemists  Power series  complex numbers and linear algebra Book
Author : Martin Cockett,Graham Doggett
Publisher : Royal Society of Chemistry
Release : 2003
ISBN : 9780854044955
Language : En, Es, Fr & De

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Book Description :

An excellent resource for all undergraduate chemistry students but particularly focussed on the needs of students who may not have studied mathematics beyond GCSE level (or equiv).

Algebraic Geometry over the Complex Numbers

Algebraic Geometry over the Complex Numbers Book
Author : Donu Arapura
Publisher : Springer Science & Business Media
Release : 2012-02-15
ISBN : 1461418097
Language : En, Es, Fr & De

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Book Description :

This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject. It covers sheaf theory, cohomology, some Hodge theory, as well as some of the more algebraic aspects of algebraic geometry. The author frequently refers the reader if the treatment of a certain topic is readily available elsewhere but goes into considerable detail on topics for which his treatment puts a twist or a more transparent viewpoint. His cases of exploration and are chosen very carefully and deliberately. The textbook achieves its purpose of taking new students of complex algebraic geometry through this a deep yet broad introduction to a vast subject, eventually bringing them to the forefront of the topic via a non-intimidating style.

Complex Numbers

Complex Numbers Book
Author : S C Roy
Publisher : Elsevier
Release : 2007-07-01
ISBN : 0857099426
Language : En, Es, Fr & De

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Book Description :

An informative and useful account of complex numbers that includes historical anecdotes, ideas for further research, outlines of theory and a detailed analysis of the ever-elusory Riemann hypothesis. Stephen Roy assumes no detailed mathematical knowledge on the part of the reader and provides a fascinating description of the use of this fundamental idea within the two subject areas of lattice simulation and number theory. Complex Numbers offers a fresh and critical approach to research-based implementation of the mathematical concept of imaginary numbers. Detailed coverage includes: Riemann’s zeta function: an investigation of the non-trivial roots by Euler-Maclaurin summation. Basic theory: logarithms, indices, arithmetic and integration procedures are described. Lattice simulation: the role of complex numbers in Paul Ewald’s important work of the I 920s is analysed. Mangoldt’s study of the xi function: close attention is given to the derivation of N(T) formulae by contour integration. Analytical calculations: used extensively to illustrate important theoretical aspects. Glossary: over 80 terms included in the text are defined. Offers a fresh and critical approach to the research-based implication of complex numbers Includes historical anecdotes, ideas for further research, outlines of theory and a detailed analysis of the Riemann hypothesis Bridges any gaps that might exist between the two worlds of lattice sums and number theory

Complex Numbers in n Dimensions

Complex Numbers in n Dimensions Book
Author : S. Olariu
Publisher : Elsevier
Release : 2002-06-20
ISBN : 9780080529585
Language : En, Es, Fr & De

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Book Description :

Two distinct systems of hypercomplex numbers in n dimensions are introduced in this book, for which the multiplication is associative and commutative, and which are rich enough in properties such that exponential and trigonometric forms exist and the concepts of analytic n-complex function, contour integration and residue can be defined. The first type of hypercomplex numbers, called polar hypercomplex numbers, is characterized by the presence in an even number of dimensions greater or equal to 4 of two polar axes, and by the presence in an odd number of dimensions of one polar axis. The other type of hypercomplex numbers exists as a distinct entity only when the number of dimensions n of the space is even, and since the position of a point is specified with the aid of n/2-1 planar angles, these numbers have been called planar hypercomplex numbers. The development of the concept of analytic functions of hypercomplex variables was rendered possible by the existence of an exponential form of the n-complex numbers. Azimuthal angles, which are cyclic variables, appear in these forms at the exponent, and lead to the concept of n-dimensional hypercomplex residue. Expressions are given for the elementary functions of n-complex variable. In particular, the exponential function of an n-complex number is expanded in terms of functions called in this book n-dimensional cosexponential functions of the polar and respectively planar type, which are generalizations to n dimensions of the sine, cosine and exponential functions. In the case of polar complex numbers, a polynomial can be written as a product of linear or quadratic factors, although it is interesting that several factorizations are in general possible. In the case of planar hypercomplex numbers, a polynomial can always be written as a product of linear factors, although, again, several factorizations are in general possible. The book presents a detailed analysis of the hypercomplex numbers in 2, 3 and 4 dimensions, then presents the properties of hypercomplex numbers in 5 and 6 dimensions, and it continues with a detailed analysis of polar and planar hypercomplex numbers in n dimensions. The essence of this book is the interplay between the algebraic, the geometric and the analytic facets of the relations.

Complex Numbers in Geometry

Complex Numbers in Geometry Book
Author : I. M. Yaglom
Publisher : Academic Press
Release : 2014-05-12
ISBN : 148326663X
Language : En, Es, Fr & De

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Book Description :

Complex Numbers in Geometry focuses on the principles, interrelations, and applications of geometry and algebra. The book first offers information on the types and geometrical interpretation of complex numbers. Topics include interpretation of ordinary complex numbers in the Lobachevskii plane; double numbers as oriented lines of the Lobachevskii plane; dual numbers as oriented lines of a plane; most general complex numbers; and double, hypercomplex, and dual numbers. The text then takes a look at circular transformations and circular geometry, including ordinary circular transformations, axial circular transformations of the Lobachevskii plane, circular transformations of the Lobachevskii plane, axial circular transformations, and ordinary circular transformations. The manuscript is intended for pupils in high schools and students in the mathematics departments of universities and teachers' colleges. The publication is also useful in the work of mathematical societies and teachers of mathematics in junior high and high schools.

John and Betty s Journey Through Complex Numbers

John and Betty s Journey Through Complex Numbers Book
Author : Matt Bower
Publisher : Matthew Bower
Release : 1999
ISBN : 9780646385204
Language : En, Es, Fr & De

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Book Description :

Set in the genre of a children's book, John and Betty trace the evolution of complex numbers and explore their operations. From integers, to fractions, to surds, complex numbers are made to seem like an obvious extension. Incorporating graphing on the complex number plane and culminating in De Moivre's Theorem, the logic of complex numbers is made to seem intuitive and simple. John and Betty delight in their journey, as will senior mathematics students.

Complex Numbers from A to Z

Complex Numbers from A to     Z Book
Author : Titu Andreescu,Dorin Andrica
Publisher : Springer Science & Business Media
Release : 2014-02-17
ISBN : 0817684158
Language : En, Es, Fr & De

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Book Description :

* Learn how complex numbers may be used to solve algebraic equations, as well as their geometric interpretation * Theoretical aspects are augmented with rich exercises and problems at various levels of difficulty * A special feature is a selection of outstanding Olympiad problems solved by employing the methods presented * May serve as an engaging supplemental text for an introductory undergrad course on complex numbers or number theory

Introduction to the Geometry of Complex Numbers

Introduction to the Geometry of Complex Numbers Book
Author : Roland Deaux
Publisher : Courier Corporation
Release : 2013-01-23
ISBN : 0486158047
Language : En, Es, Fr & De

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Book Description :

Geared toward readers unfamiliar with complex numbers, this text explains how to solve problems that frequently arise in the applied sciences and emphasizes constructions related to algebraic operations. 1956 edition.