Well, I went through 5 years of electrical engineering which is almost entirely in the realm of complex numbers and I’m struggling to convey my intuition here t

Well, I went through 5 years of electrical engineering which is almost entirely in the realm of complex numbers and I’m struggling to convey my intuition here to you. I think it’s helpful to understand that complex numbers are two dimensional but they aren’t like an [x,y] where the two dimensions are completely 100% unrelated. Here’s another way to think about it in a way that is familiar to you that I haven’t seen anyone else post yet. Imagine natural numbers like 1,2,3… and so on. Now imagine those are just a subset or special case of fractional numbers like 1/2,4/3,… Those fractional (rational) numbers are expressed in terms of two natural numbers. Now in the past they couldn’t solve all equations because they were frustrated that some numbers couldn’t be expressed as fractions. They called these irrationals. But irrational numbers can be expressed as an infinite sum of rational numbers. This includes numbers like pi and e. Next you can make all those irrational and rational (real Numbers) to be negative. And then that’s still not the end of it because there’s more gaps! We need complex numbers :) Then after complex you can go into tensor spaces like real^(3x3) where numbers are more like matrices. Perhaps the easiest to understand is a space of (r,g,b). Each pixel has an x,y coordinate but each point is vector valued (3 natural numbers on the range of 0-255). It should be easy to also visualize a complex number space of the same nature but with different properties. Perhaps the best equation to understand complex numbers is Euler’s equation e^(ix) = cos(x) + isin(x) Or if you put in pi you end up with the most beautiful equation ever. e^(i*pi)-1=0