Discovery of Complex numbers
DOI:
https://doi.org/10.54097/hset.v38i.5785Keywords:
Complex numbers, cubic equation, complex set and topolgy.Abstract
A branch of mathematical analysis called complex analysis studies the functions of complex numbers. It is also sometimes referred to as the theory of functions of a complex variable. Complex analysis has been used extensively in mathematics, physics, and engineering over the years, particularly in the areas of algebraic geometry, fluid dynamics, quantum mechanics, and other related fields. It dates back to the 16th century, when Italian mathematicians Girolamo Cardano and Raphael Bombelli first noticed complex numbers while attempting to solve a particular algebra, and was later developed by Cauchy and Riemann in the 19th century. The development of complex numbers has a lengthy history. Mathematicians have advanced the discipline of mathematics significantly after thousands of years of development. During this time, mathematicians also found a great deal of previously unknown mathematical information and proved formulae and phenomena that had previously been impossible to verify. And it covers complex numbers as well as some of the mathematics related to them. In this paper, the complete discovery of complex numbers from cubic equation to topology of complex numbers is detailedly revealed.
Downloads
References
Liu Shenghua, Pan Jifu, Zheng Jiyun, complex change function [M]. Changchun: Jilin Education Press,1988。
Zhong Yuquan, complex function Theory (second edition) [M]. Beijing: Higher Education Press, 1988.
L V Alforth, complex analysis [M]. Shanghai: Shanghai Science Press, 1984.
Tan Xiaohong, Wu Shengjian complex change function concise tutorial [M]. Beijing: Peking University Press, 2006.
Jerrld E Maislen, Basic complex analysis [M]. Freeman W H and Company, 1973.
A Simple Proof of the Fundamental Cauchy-Goursat Theorem, Eliakim Hastings Moore, American Mathematical Society.
Complex variables and applications / James Ward Brown, Ruel V. Churchill.—9th ed. 1221 Avenue of the Americas, New York, NY 10020.
Matrices, Faculty of Mathematics Centre for Education in Waterloo, Ontario N2L 3G1.
Integration along curves, VED V. DATAR.
The Cauchy–Riemann Equations, Joel Feldman, 2012.
Cauchy’s integral formula, Jeremy Orlof.
Taylor’s Theorem and Applications, James S. Cook, November 11, 2018, For Math 132 Online.
Taylor & Laurent theorem, Chandan kumar Department of physics S N Sinha College Jehanabad Introduction.
Complex Analysis, Elias M. Stein and Rami Shakarchi, published by Princeton University Press and copyrighted, © 2003.
A Formal Proof of Cauchy’s Residue Theorem, Wenda Li and Lawrence C. Paulson Computer Laboratory, University of Cambridge.
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
