Complex number and point-set topology

Junchi Yang; Yunyang Ye; Chengyue zhang; Hongrun Li

doi:10.1117/12.2628084

22 April 2022 Complex number and point-set topology

Junchi Yang, Yunyang Ye, Chengyue zhang, Hongrun Li

Proceedings Volume 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021); 1216340 (2022) https://doi.org/10.1117/12.2628084
Event: International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 2021, Nanjing, China

Abstract

Complex numbers, is an important part of modern mathematics. By using the complex number, we can solve many geometry problems. However, it can also be applied to physics. For example, it can play an important role in calculating alternating current. In this paper, we will introduce the definition and several properties of the complex number, also including the point-set topology. We try to prove the important theorems about the complex number; for instance, de Moivre's formula, the problems of connected set and path-connected set; also, the main idea that we cannot compare two complex numbers. To achieve these goals, we will use induction, Euler’s formula; the basic concept of topology, and proving by contradiction.

Citation Download Citation

Junchi Yang, Yunyang Ye, Chengyue zhang, and Hongrun Li "Complex number and point-set topology", Proc. SPIE 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 1216340 (22 April 2022); https://doi.org/10.1117/12.2628084

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