Complex numbers are everywhere. From signal processing and circuit analysis all the way to quantum mechanics and fluid dynamics, the imaginary unit, i, seems to be dominating most of the equations in engineering and physics. But how can that be? How can a number so seemingly arbitrary such as i with no obvious real-world interpretation be as useful as it is?
The imaginary unit whose symbol is i, or j for electrical engineers, is defined as the square root of negative one.
But didn’t we all learn in high school that one simply cannot define the square root of a negative number? It is true that when someone first comes across the concept of the imaginary unit is filled with doubt and suspicion. In order to understand its significance, however, I will ask you — in the context of this article — to pretend to forget everything you know about mathematics. I will offer you an additional way to look at the science of mathematics, one that makes complex numbers not only desirable but necessary. Let’s begin!
Mathematical Formalism
Mathematical Formalism is one of the main theories in the philosophy of mathematics.
According to formalism, all mathematics can be reduced to rules for manipulating formulas without any reference to the meanings of the…
