^Same here, I have taken countless tests using imaginary numbers, but it never went beyond a really pointless exercise in my mind. Now I get it.

It's a shame I paid for all that college and knowing this would have greatly expanded my understanding of a lot of what I learned in my math classes.

EDIT: I guess I learned it in high school though, and the math teacher probably didn't know this either.

Point being, everyone should come across this at some point. It would be beneficial to many math students.

Back in school, about halfway through my course in DSP, my teacher realized that none of us had any idea what he was talking about...so he went back to basics and explained Imaginary numbers much like this article for a whole day. Things started to make a lot more sense after that, but he was shocked that nobody had taught us that in any of our classes before.

Thanks! I took several college courses using them and didn't "get" the concept until years after I graduated.

Luckily, my AC circuits class was basically the applied version of this article, with lots of conversions between the complex and phase-amplitude descriptions.

What blew my mind at the time was the exponential notation for the unit phasor: e^(i * x). It turns out that e^(i * x) = cos(x) + i * sin(x) because that's just the way the math works out, and it's trivial to work it out yourself by looking at the Taylor series expansions of the three terms.