Complex numbers in N dimensions /

Complex numbers in N dimensions /

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...

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Bibliographic Details
Main Author: Olariu, Silviu
Format: Electronic eBook
Language:English
Published: Amsterdam ; Boston : Elsevier, 2002.
Edition:1st ed.
Series:North-Holland mathematics studies ; 190.
Subjects:
Numbers, Complex.
Online Access:CONNECT
Table of Contents:
  • Cover
  • Contents
  • Chapter 1. Hyperbolic Complex Numbers in Two Dimensions
  • 1.1 Operations with hyperbolic twocomplex numbers
  • 1.2 Geometric representation of hyperbolictwocomplex numbers
  • 1.3 Exponential and trigonometric forms of a twocomplex number
  • 1.4 Elementary functions of a twocomplex variable
  • 1.5 Twocomplex power series
  • 1.6 Analytic functions of twocomplex variables
  • 1.7 Integrals of twocomplex functions
  • 1.8 Factorization of twocomplex polynomials
  • 1.9 Representation of hyperbolic twocomplex numbers by irreducible matrices
  • Chapter 2. Complex Numbers in Three Dimensions
  • 2.1 Operations with tricomplex numbers
  • 2.2 Geometric representation of tricomplex numbers
  • 2.3 The tricomplex cosexponential functions
  • 2.4 Exponential and trigonometric forms of tricomplex numbers
  • 2.5 Elementary functions of a tricomplex variable
  • 2.6 Tricomplex power series
  • 2.7 Analytic functions of tricomplex variables
  • 2.8 Integrals of tricomplex functions
  • 2.9 Factorization of tricomplex polynomials
  • 2.10 Representation of tricomplex numbers by irreducible matrices
  • Chapter 3. Commutative Complex Numbers in Four Dimensions
  • 3.1 Circular complex numbers in four dimensions
  • 3.2 Hyperbolic complex numbers in four dimensions
  • 3.3 Planar complex numbers in four dimensions
  • 3.4 Polar complex numbers in four dimensions
  • Chapter 4. Complex Numbers in 5 Dimensions
  • 4.1 Operations with polar complex numbers in 5 dimensions
  • 4.2 Geometric representation of polar complex numbers in 5 dimensions
  • 4.3 The polar 5-dimensional cosexponential functions
  • 4.4 Exponential and trigonometric forms of polar 5-complex numbers
  • 4.5 Elementary functions of a polar 5-complex variable
  • 4.6 Power series of 5-complex numbers
  • 4.7 Analytic functions of a polar 5-complex variable
  • 4.8 Integrals of polar 5-complex functions
  • 4.9 Factorization of polar 5-complex polynomials
  • 4.10 Representation of polar 5-complex numbers by irreducible matrices
  • Chapter 5. Complex Numbers in 6 Dimensions
  • 5.1 Polar complex numbers in 6 dimensions
  • 5.2 Planar complex numbers in 6 dimensions
  • Chapter 6. Commutative Complex Numbers in n Dimensions
  • 6.1 Polar complex numbers in n dimensions
  • 6.2 Planar complex numbers in even n dimensions
  • Bibliography
  • Index
  • Last Page.

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