Theoretical and Natural Science

Theoretical and Natural Science

TNS Vol.1 No.1, 05 May 2022

Open Access | Article

Elegant Theory of Complex Analysis

Yisun Chen 1
1 Shanghai Foreign Language School Affiliated to SISU

* Author to whom correspondence should be addressed.

Theoretical and Natural Science, TNS Vol.1 No.1, 30-37
Published 05 May 2022. © 2023 The Author(s). Published by EWA Publishing
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Citation Yisun Chen. Elegant Theory of Complex Analysis. TNS (2022) TNS Vol.1 No.1: 30-37. DOI: 10.54254/tns.2022005.


A complex number is an element in a number system containing both real numbers and the imaginary unit 𝑖, satisfying 𝑖^2 = −1. Since their discovery, complex numbers have been a powerful means of mathematical calculation. Complex analysis is a part of mathematical analysis that investigates complex numbers and their analyticity, holomorphicity, etc. Many renowned mathematical giants once had their own research in complex analysis, such as Cauchy, Gauss, Euler, etc. On the grounds that it deals with functions of complex numbers, complex analysis is a helpful area in the whole mathematics field. There are plenty of applications of complex analysis in both the mathematical field and the physics field. In this paper, the history of complex numbers and complex analysis is presented. Also, some contents of complex variables are shown, including the basic properties of complex numbers, the derivative and integral of functions of complex numbers, and several critical theorems in the area of complex analysis.


Complex variables, Complex analysis, Complex number


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Data Availability

The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.

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