One of my favorite things in mathematics is imaginary numbers. Such a ridiculous name for something so important. I prefer the name complex numbers.
You probably haven’t seen an imaginary number since you were in school. The first time that you encounter i is when learning to solve quadratic equations. You’ll find them in the quadratic formula when there is a negative number under the square root sign.
Let a, b, and c be real number. The solutions of are
So if we end up with a solution like
We can re-write it as
This is about as far as it goes for most people. I remember being delighted to learn about complex numbers. Then saddened that they disappeared from my life as soon as they had entered. I would see them again.
Rediscovering Complex Numbers
The only thing in physics that I liked was problems of electricity. To this day my favorite equations are Maxwell’s equations of electromagnetism. I am amazed that so few equations represent all you need to know. I was surprised to see that complex numbers make a reappearance when solving these types of problems. I just remember that being able to do this and breaking things down into component vectors allows us to solve them.
This is a terrible explanation. Unfortunately, I couldn’t find any basic videos for solving these types of problems. Kind of wished I had my old physics textbook.
The History of Imaginary Numbers
I don’t watch that many science channels on YouTube. I am happy to stick with the mathematics channels. But, YouTube has a way of recommending things so continuously that you have to check them out. I’ve had several old Veritasium videos in my feed lately. I finally watched this one on the history of imaginary numbers.
Of course, they make the story more epic for views. See the thumbnail for what I mean. I dislike that to make math more interesting we have to make it more scandalous. I did enjoy the video though. Especially since it went over the connections between algebra and geometry.
It makes a connection to quantum mechanics and reality. Which, I think is a bit more spurious but I don’t know that much about those physics formulas. I’ve been watching rebuttals because of this. These sorts of big claims are interesting but I worry about people getting confused by them. If you don’t have a physics degree you don’t know if this claim is just clickbait or not.
One of the reasons why I don’t cover serious mathematics on this blog is because I don’t want to end up with this problem. I don’t want to make a claim that I can’t explain. That is why I’ll always defer to a source where a mathematician answers.
I’m the writer with a mathematical muse. I love words, numbers, dreaming big & helping others. I believe that whatever you imagine, you can become. They/Them.