Cubic equation and topology of complex numbers

Abstract

The study of complex analysis is an intriguing and technical topic. Over the past few centuries, mathematicians have produced ground-breaking work in this field. Mathematicians initially defined complex numbers, and then they gradually investigated their algebraic and geometric properties. They stumbled upon and researched intricate calculations hundreds of years later. The solution of the cubic equation has motivated mathematicians to explore the study of complex numbers, but it has also advanced mathematics in many other ways by exposing previously undiscovered issues. First off, when there are multiple real roots to the equation, it is impossible to obtain all of them using Cardano's formula at that time without understanding the fundamentals of complex numbers. Therefore, when they test various examples, mathematicians occasionally discover that there are other roots that are quite clear but are impossible to pass via Cardano's formula. In this paper, it start from the research of cubic equaiton and then discuss in detail topology of complex numbers.