This is the most confusing thing for math students.
Channel: Jake Bruner
Date: 2022-04-28

Note: at 1:11 I meant to say "alpha prime" not "a prime." I probably should have used another letter in hindsight.

In this short video, I delve into the fascinating concept that is complex numbers. In high school, students are typically offered a brief introduction to their addition and multiplication (and sometimes a tad bit more). I know from personal experience that people often leave algebra II with the feeling that complex numbers are some useless, made-up concept. I think that, unfortunately, understanding the true significance of the complex number requires getting into the weeds of a lot of formal math concepts which seem incredibly opaque. Because of this, I intended to give a brief overview (and perhaps a bit of an oversimplification) of some abstract algebra concepts in order to get at complex number's uniqueness. Namely that they are one of three real (finite) division algebras, they're the only 2-dimensional unital algebra to form a field, and they encode intuitive properties about 2-d euclidean space. I also wanted to take a look at the alternative definitions of the complex numbers and perhaps hint at the concept of isomorphism (which I can proudly say I didn't mention once in the video!). Either way, I would love any thoughts, feedback or corrections; I have never tried my hand at a math video like this before.