Newton-Leibniz Formula Based on the Decomposition Method of Split Complex Zero Factors

Abstract

Extending the classical results in real analysis to the split complex plane is currently a very active area of mathematical research, with numerous scholars conducting extensive studies in this field. This paper investigates the Newton-Leibniz formula on the split complex plane, where split complex numbers form a commutative ring with zero divisors generated by two real numbers. By overcoming the challenge posed by the presence of zero divisors in split complex numbers, this study derives the Newton-Leibniz formula on the hyperbolic plane through the factorization of zero divisors in split complex numbers. This work lays a theoretical foundation for split complex analysis and provides impetus for the development of physics grounded in the context of categorical complex analysis. This work will also establish a research foundation and inject momentum into further investigations into four-dimensional space models utilizing the split complex numbers.