Version 1
: Received: 18 December 2023 / Approved: 19 December 2023 / Online: 19 December 2023 (08:01:08 CET)
How to cite:
Jean Paul, P.; Wahid, S. Semi-Structured Complex Numbers:Extending the Cauchy–Riemann Equations and developing Semi-Structured Complex Analytic Functions. Preprints2023, 2023121403. https://doi.org/10.20944/preprints202312.1403.v1
Jean Paul, P.; Wahid, S. Semi-Structured Complex Numbers:Extending the Cauchy–Riemann Equations and developing Semi-Structured Complex Analytic Functions. Preprints 2023, 2023121403. https://doi.org/10.20944/preprints202312.1403.v1
Jean Paul, P.; Wahid, S. Semi-Structured Complex Numbers:Extending the Cauchy–Riemann Equations and developing Semi-Structured Complex Analytic Functions. Preprints2023, 2023121403. https://doi.org/10.20944/preprints202312.1403.v1
APA Style
Jean Paul, P., & Wahid, S. (2023). Semi-Structured Complex Numbers:Extending the Cauchy–Riemann Equations and developing Semi-Structured Complex Analytic Functions. Preprints. https://doi.org/10.20944/preprints202312.1403.v1
Chicago/Turabian Style
Jean Paul, P. and Shanaz Wahid. 2023 "Semi-Structured Complex Numbers:Extending the Cauchy–Riemann Equations and developing Semi-Structured Complex Analytic Functions" Preprints. https://doi.org/10.20944/preprints202312.1403.v1
Abstract
Real and complex analytic functions are largely studied in the field of complex analysis and are seen as very useful tools in solving problems in mathematics, physics and engineering. Real and complex numbers are a subset of semi-structured complex numbers (a new number set created to algebraically solve division by zero). Nevertheless, the properties of analytic functions made up of semi-structured complex variables (called semi-structured complex analytic functions) is yet to be explored. This limits the range of possible problems that can be resolved using analytic functions). In this regard, the aim of this paper was to expound upon the properties of semi-structured complex analytic functions and show their application in solving engineering problems. The results of this paper included (1) developing a full set of Cauchy–Riemann Equations for the semi-structured complex -space; (2) define sufficient and necessary conditions for a semi-structured complex function to be analytic; (3) determine the relationship between semi-structured complex analytic functions, Laplace’s Equations and Poisson’s Equations; and (5) provide an example of the use of these functions.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
