Complex Numbers and Geometry

Complex Numbers and Geometry
Author: Liang-shin Hahn
Publsiher: American Mathematical Soc.
Total Pages: 192
Release: 2019-12-26
ISBN 10: 1470451824
ISBN 13: 9781470451820
Language: EN, FR, DE, ES & NL

Complex Numbers and Geometry Book Review:

The purpose of this book is to demonstrate that complex numbers and geometry can be blended together beautifully. This results in easy proofs and natural generalizations of many theorems in plane geometry, such as the Napoleon theorem, the Ptolemy-Euler theorem, the Simson theorem, and the Morley theorem. The book is self-contained—no background in complex numbers is assumed—and can be covered at a leisurely pace in a one-semester course. Many of the chapters can be read independently. Over 100 exercises are included. The book would be suitable as a text for a geometry course, or for a problem solving seminar, or as enrichment for the student who wants to know more.

Complex Numbers and Vectors

Complex Numbers and Vectors
Author: Les Evans
Publsiher: Aust Council for Ed Research
Total Pages: 168
Release: 2006
ISBN 10: 0864315325
ISBN 13: 9780864315328
Language: EN, FR, DE, ES & NL

Complex Numbers and Vectors Book Review:

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.

Geometry of Complex Numbers

Geometry of Complex Numbers
Author: Hans Schwerdtfeger
Publsiher: Courier Corporation
Total Pages: 224
Release: 2012-05-23
ISBN 10: 0486135861
ISBN 13: 9780486135861
Language: EN, FR, DE, ES & NL

Geometry of Complex Numbers Book Review:

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

Complex Numbers from A to Z

Complex Numbers from A to    Z
Author: Titu Andreescu,Dorin Andrica
Publsiher: Springer Science & Business Media
Total Pages: 322
Release: 2007-10-08
ISBN 10: 0817644490
ISBN 13: 9780817644499
Language: EN, FR, DE, ES & NL

Complex Numbers from A to Z Book Review:

* 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

Maths for Chemists Power series complex numbers and linear algebra

Maths for Chemists  Power series  complex numbers and linear algebra
Author: Martin Cockett,Graham Doggett
Publsiher: Royal Society of Chemistry
Total Pages: 143
Release: 2003
ISBN 10: 9780854044955
ISBN 13: 0854044957
Language: EN, FR, DE, ES & NL

Maths for Chemists Power series complex numbers and linear algebra Book Review:

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).

Pure mathematics

Pure mathematics
Author: Anthony Nicolaides
Publsiher: PASS PUBLICATIONS
Total Pages: 89
Release: 2007
ISBN 10: 1872684920
ISBN 13: 9781872684925
Language: EN, FR, DE, ES & NL

Pure mathematics Book Review:

Around Caspar Wessel and the Geometric Representation of Complex Numbers

Around Caspar Wessel and the Geometric Representation of Complex Numbers
Author: Jesper Lützen
Publsiher: Kgl. Danske Videnskabernes Selskab
Total Pages: 293
Release: 2001
ISBN 10: 9788778762368
ISBN 13: 8778762367
Language: EN, FR, DE, ES & NL

Around Caspar Wessel and the Geometric Representation of Complex Numbers Book Review:

Calculus with Complex Numbers

Calculus with Complex Numbers
Author: John B. Reade
Publsiher: CRC Press
Total Pages: 112
Release: 2003-03-13
ISBN 10: 9780203417867
ISBN 13: 0203417860
Language: EN, FR, DE, ES & NL

Calculus with Complex Numbers Book Review:

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 Theo

Complex Numbers

Complex Numbers
Author: Walter Ledermann
Publsiher: Springer Science & Business Media
Total Pages: 63
Release: 2013-03-14
ISBN 10: 940116570X
ISBN 13: 9789401165709
Language: EN, FR, DE, ES & NL

Complex Numbers Book Review:

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.

Complex Numbers

Complex Numbers
Author: S C Roy
Publsiher: Elsevier
Total Pages: 144
Release: 2007-07-01
ISBN 10: 0857099426
ISBN 13: 9780857099426
Language: EN, FR, DE, ES & NL

Complex Numbers Book Review:

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
Author: S. Olariu
Publsiher: Elsevier
Total Pages: 286
Release: 2002-06-20
ISBN 10: 9780080529585
ISBN 13: 0080529585
Language: EN, FR, DE, ES & NL

Complex Numbers in n Dimensions Book Review:

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
Author: I. M. Yaglom
Publsiher: Academic Press
Total Pages: 256
Release: 2014-05-12
ISBN 10: 148326663X
ISBN 13: 9781483266633
Language: EN, FR, DE, ES & NL

Complex Numbers in Geometry Book Review:

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.

Complex Numbers Made Simple

Complex Numbers Made Simple
Author: Verity Carr
Publsiher: Newnes
Total Pages: 128
Release: 1996-03-12
ISBN 10: 0080938442
ISBN 13: 9780080938448
Language: EN, FR, DE, ES & NL

Complex Numbers Made Simple Book Review:

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.

Finite Neutrosophic Complex Numbers

Finite Neutrosophic Complex Numbers
Author: W. B. Vasantha Kandasamy, Florentin Smarandache
Publsiher: Infinite Study
Total Pages: 219
Release: 2011
ISBN 10: 1599731584
ISBN 13: 9781599731582
Language: EN, FR, DE, ES & NL

Finite Neutrosophic Complex Numbers Book Review:

Algebraic Geometry over the Complex Numbers

Algebraic Geometry over the Complex Numbers
Author: Donu Arapura
Publsiher: Springer Science & Business Media
Total Pages: 329
Release: 2012-02-15
ISBN 10: 1461418097
ISBN 13: 9781461418092
Language: EN, FR, DE, ES & NL

Algebraic Geometry over the Complex Numbers Book Review:

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.

Non Associative Algebraic Structures Using Finite Complex Numbers

Non Associative Algebraic Structures Using Finite Complex Numbers
Author: W.B. Vasantha Kandasamy, Florentin Smarandache
Publsiher: Infinite Study
Total Pages: 329
Release: 2012
ISBN 10: 159973169X
ISBN 13: 9781599731698
Language: EN, FR, DE, ES & NL

Non Associative Algebraic Structures Using Finite Complex Numbers Book Review:

The authors have used the concept of finite complex modulo integers to construct non associative algebraic structures like groupoids, loops and quasi-loops.Using these structures we built non associative complex matrix groupoids and complex polynomial groupoids.The authors suggest over 300 problems and some are at the research level.

Exploring the Extension of Natural Operations on Intervals Matrices and Complex Numbers

Exploring the Extension of Natural Operations on Intervals  Matrices and Complex Numbers
Author: W. B. Vasantha Kandasamy, Florentin Smarandache
Publsiher: Infinite Study
Total Pages: 150
Release: 2012
ISBN 10: 1599731797
ISBN 13: 9781599731797
Language: EN, FR, DE, ES & NL

Exploring the Extension of Natural Operations on Intervals Matrices and Complex Numbers Book Review:

In this book we explore the possibility of extending the natural operations on reals to intervals and matrices. The extension to intervals makes us define a natural class of intervals in which we accept [a, b], a greater than b. Further, we introduce a complex modulo integer in Z_n (n, a positive integer) and denote it by iF with iF^2 = n-1.

Ten Decimal Tables of the Logarithms of Complex Numbers and for the Transformation from Cartesian to Polar Coordinates

Ten Decimal Tables of the Logarithms of Complex Numbers and for the Transformation from Cartesian to Polar Coordinates
Author: L. A. Lyusternik
Publsiher: Elsevier
Total Pages: 128
Release: 2014-06-20
ISBN 10: 1483184978
ISBN 13: 9781483184975
Language: EN, FR, DE, ES & NL

Ten Decimal Tables of the Logarithms of Complex Numbers and for the Transformation from Cartesian to Polar Coordinates Book Review:

Ten-Decimal Tables of the Logarithms of Complex Numbers and for the Transformation from Cartesian to Polar Coordinates contains Tables of mathematical functions up to ten-decimal value. These tables are compiled in the Department for Approximate Computations of the Institute of Exact Mechanics and Computational Methods of the U.S.S.R. Academy of Sciences. The computations are carried out by this department in conjunction with the Computational-Experimental Laboratory of the Institute. This book will be of value to mathematicians and researchers.

Complex Numbers

Complex Numbers
Author: Glen Prideaux
Publsiher: Lulu.com
Total Pages: 104
Release: 2016-09-27
ISBN 10: 1365424898
ISBN 13: 9781365424892
Language: EN, FR, DE, ES & NL

Complex Numbers Book Review:

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 Analysis

Complex Analysis
Author: Joseph Bak,Donald J. Newman
Publsiher: Springer Science & Business Media
Total Pages: 296
Release: 1999-06-25
ISBN 10: 9780387947563
ISBN 13: 0387947566
Language: EN, FR, DE, ES & NL

Complex Analysis Book Review:

This unusually lively textbook introduces the theory of analytic functions, explores its diverse applications and shows the reader how to harness its powerful techniques. The book offers new and interesting motivations for classical results and introduces related topics that do not appear in this form in other texts. For the second edition, the authors have revised some of the existing material and have provided new exercises and solutions.