An Introduction to Complex Analysis and Applications
An Introduction to Complex Analysis and Applications How imaginary numbers have a real impact. Figure 1: A representation of a Complex Function. These can be created once you understand what a complex function is. The Color represents the argument of the complex function, while the brightness/hue is represented by the magnitude. Image Citation: Creative Commons. Introduction: Let us start easy. What is the square root of 100? In other words, what number times itself is equal to 100? Easy, the answer is 10. What is the square root of -1? Well that isn’t so obvious. Since a negative number times a negative number is positive, how is it possible that we can solve for the square root of -1? The answer is; we define it. And this isn’t just a trivial definition. Assigning this answer, i , the ‘imaginary unit’ is the beginning step of a beautiful and deep field, known as complex analysis. So, why should you care about complex analysis? It turns out, t...