Complex Analysis and its Several Applications

Abstract

Complex analysis is important for science because it extends analytical methods from real variables to complex variables and complex numbers. Also, complex number has two independent components, one variable will not change when the other is changing, that are particularly useful when two variables must be dealt with simultaneously. In this essay, we are going to talk about the history chronologically such as who first introduced the idea of complex number, who first discovered the rule of complex number, and why complex analysis is important. Also, the essay includes some basics about the complex variable and complex analysis. For example, the definition of complex number, Cauchy-Riemann Equations, and Cauchy Goursat theorem can help us to get further known of the complex analysis and solve some basic analytic problems.