Geometric and topological structures of complex numbers

Li Lei; LongTing Wang

doi:10.1117/12.2628101

22 April 2022 Geometric and topological structures of complex numbers

Li Lei, LongTing Wang

Proceedings Volume 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021); 121633L (2022) https://doi.org/10.1117/12.2628101
Event: International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 2021, Nanjing, China

Abstract

When remarking on the results in this field of mathematics, mathematicians and engineers are inclined to use terms like magical or even miraculous; and in exploring the topic, both mathematicians and engineers continue to be amazed by the beauty and sweep of the conclusions. One of the algebraically closed number systems that include all real numbers is the complex number field. This article focuses on the geometric and algebraic structures of complex numbers, such as their definition and arithmetic operations and the field and polar form. In order to elaborate on connections between complex numbers and trigonometry, the de Moivre’s Formula, as one of important results in the world of complex numbers, is discussed. Topological properties of the complex plane are also discussed in this paper.

Citation Download Citation

Li Lei and LongTing Wang "Geometric and topological structures of complex numbers", Proc. SPIE 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 121633L (22 April 2022); https://doi.org/10.1117/12.2628101

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