Complex Numbers in Dimensions

Silviu Olariu (Eds.)9780444511232, 0444511237

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 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.

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Table of contents :
Content:
Preface
Pages vii-ix

Chapter 1 Hyperbolic complex numbers in two dimensions Original Research Article
Pages 1-16

Chapter 2 Complex numbers in three dimensions Original Research Article
Pages 17-50

Chapter 3 Commutative complex numbers in four dimensions Original Research Article
Pages 51-147

Chapter 4 Complex numbers in 5 dimensions Original Research Article
Pages 149-165

Chapter 5 Complex numbers in 6 dimensions Original Research Article
Pages 167-193

Chapter 6 Commutative complex numbers in n dimensions Original Research Article
Pages 195-261

Index
Pages 263-269