Complex Number
Complex Analysis for Beginners: “Everything Just Works”
An intuitive guide to some of the main features of Complex Analysis
Complex Analysis is one of the most beautiful topics in mathematics. Famously, the equation
is a first result, an underlies much of the rest of the field.
In this article, we will start by deriving this formula, using only some basic calculus, and then tour some of the most aesthetically pleasing parts of Complex Analysis. This article is written for those with at least a Calculus II background, though it could be read by someone with less if they are willing to take some claims at face value. We will cover up to the Cauchy Riemann equations and the Cauchy Integral formula, with its consequences.
Roadmap of the Article:
- Difference between imaginary and complex numbers
- Proof of Euler’s formula
- Differentiation Properties
- Integration Properties
Imaginary vs. Complex
The first, and most fundamental fact, about the complex numbers is that we assign
to be the imaginary number. Because we cannot solve all polynomials using only…
