Complex number and its discovery history
DOI:
https://doi.org/10.54097/hset.v38i.5802Keywords:
Complex Plane, Cubic equation, Complex numbers.Abstract
The operations of complex numbers are the main subject of the mathematical analysis area known as complex analysis. It is also known as the theory of functions of a complex variable. The primary research topic in the field of complex analysis is holomorphic functions. These functions are defined on the complex plane, have differentiable properties, and allow for negative values. The residue theorem, the Cauchy integral formula, the Laurent series expansion, etc. are a few concepts, ideas, and methods that are commonly used in research. In particular, over the years, complex analysis in mathematics, physics, and engineering has been extensively used in algebraic geometry, fluid dynamics, quantum mechanics, and other related areas. Two Italian mathematicians, Girolamo Cardano and Raphael Bombelli, discovered complex numbers in the 16th century while attempting to solve a particular algebra, and Cauchy and Riemann extended it in the 19th century. This essay begin with investigation of arithmetic propertity of comlex numbers and then fully explores history development of complex numbers.
Downloads
References
Lang, S., 1999. Complex analysis by Serge Lang. London: Springer-Verlag.
Stein, M. and Shakarchi, R., 2003. Princeton lectures in analysis, volume II: Complex analysis. Princeton: Princeton university press.
Brannan, D., Clunie, J. and Kirwan, W., 1973. On the coefficient problem for functions of bounded boundary rotation. Annales Academiae Scientiarum Fennicae Series A I Mathematica, 1973, pp.1-18.
Barnard, R.W. (1990). Open problems and conjectures in complex analysis. In: Ruscheweyh, S., Saff, E.B., Salinas, L.C., Varga, R.S. (eds) Computational Methods and Function Theory. Lecture Notes in Mathematics, vol 1435. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087893.
Barnard, R., Jayatilake, U. and Solynin, A., 2015. Brannan’s conjecture and trigonometric sums. Proceedings of the American Mathematical Society, 143(5), pp.2117-2128.
Aharonov, D. and Friedland, S., 1973. On an inequality connected with the coefficient conjecture for functions of bounded boundary rotation. Annales Academiae Scientiarum Fennicae Series A I Mathematica, 1973, pp.1-14.
Milcetich, J., 1989. On a coefficient conjecture of Brannan. Journal of Mathematical Analysis and Applications, 139(2), pp.515-522.
Roger W. Barnard, Kent Pearce & William Wheeler (1997) On a Coefficient Conjecture of Brannan, Complex Variables, Theory and Application: An International Journal, 33:1-4, 51-61, DOI: 10.1080/17476939708815011
Udaya C. Jayatilake (2013) Brannan's conjecture for initial coefficients, Complex Variables and Elliptic Equations, 58:5, 685-694, DOI: 10.1080/17476933.2011.605445.
Szász, R. On Brannan’s Conjecture. Mediterr. J. Math. 17, 38 (2020).
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.
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.
Taylor & Laurent theorem, Chandan kumar Department of physics S N Sinha College Jehanabad Introduction.
A Formal Proof of Cauchy’s Residue Theorem, Wenda Li and Lawrence C. Paulson Computer Laboratory, University of Cambridge.
Peters, Christen. The Reality of the Complex: The Discovery and Development of Imaginary Numbers. The College Mathematics Journal
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
