Hyperbolic complex numbers in two dimensions

Abstract

A system of commutative hyperbolic complex numbers in 2 dimensions is studied in this paper. Exponential and trigonometric forms are obtained for these hyperbolic twocomplex numbers. Expressions are given for the elementary functions of hyperbolic twocomplex variable. The functions of a hyperbolic twocomplex variable which are defined by power series are analytic. Relations of equality exist between partial derivatives of the real components a function of a hyperbolic twocomplex variable. The integral of a twocomplex function between two points is independent of the path connecting the points. A hyperbolic twocomplex polynomial can be written as a product of linear or quadratic factors, although the factorization may not be unique.