Exploring the Applications and Properties of Complex Numbers in Mathematical Analysis

Abstract

Complex numbers, a cornerstone of mathematical theory, have found widespread application in various branches of science and engineering. This research paper delves into the multifaceted nature of complex numbers, investigating their fundamental properties and exploring their diverse applications in mathematical analysis. We begin by elucidating the structure of complex numbers, highlighting their algebraic, geometric, and analytical aspects. Subsequently, we delve into the applications of complex numbers in solving polynomial equations, differential equations, and integral transforms, showcasing their efficacy in providing elegant solutions to complex problems. Moreover, we examine the role of complex numbers in representing and analyzing periodic phenomena through Fourier analysis and signal processing. Furthermore, we explore the connections between complex numbers and other mathematical concepts, such as geometry, calculus, and number theory, illustrating their versatility and profound influence across different domains. Through a comprehensive examination of the applications and properties of complex numbers, this paper aims to deepen our understanding of their significance in mathematical analysis and inspire further research in this rich and captivating field.

Cite as:

Vaibhav Bagal. (2024). Exploring the Applications and Properties of Complex Numbers in Mathematical Analysis. Journal of Applied Mathematics and Statistical Analysis, 5(1), 10–13. https://doi.org/10.5281/zenodo.10886720