I’ve been working with imaginary numbers on and off for several years now. I know the operations, but I have no understanding of them whatsoever. I was taught in my freshman year of highschool that they “are useful in advanced math/engineering” and was instructed to memorize the operations. Well here I am, 7 years later doing advanced math/engineering without any intuition for what they do. I am trying to learn quaternions, which build upon imaginary numbers. I figure it’s nigh time I start to get an understanding of what they do & their purpose.
I wanted a visual understanding, so I taught myself using this site:
A Visual, Intuitive Guide to Imaginary Numbers – BetterExplained
I like the idea that imaginary numbers are not special. They are a mathematical construct that is useful for describing the world around us. They make math easier.
Negative numbers are very similar. How can you have less than nothing? It doesn’t make any sense. Yet, the negative sign is very useful for signifying direction without have to prefix every number with a sentence for context. Consider a bank account. We all know what it means to have -100$ in an account. This helps us avoid having to say I owe the bank 100$.
Imaginary numbers, similar to negative numbers are a mathematical construct that is useful for describing the world around us. They are useful fiction.