>You two are both math savants so maybe one of you can explain something to me. It is i, the square root of negative 1. Dumbo me finally asked a professor about it. I said the square of anything is a positive. He said that's true in theory but i makes possible many theorems. That was when I knew I had no trajectory in advanced mathematics.

Saying "square of anything is a positive" is like saying "anything with wheels is a vehicle"... which works splendidly while you're watching the road. But if you look around you may find a sliding door, or a mechanical clock, or a toy... all of which have wheels but aren't vehicles.

"Square of anything is a positive" is still true if you stay within the set of real numbers. If you look at it in a wider set of complex numbers, for most of them "positive" doesn't even have a meaning, but they can still be squared, you just don't get a real number as a result in most cases, you get another complex number.

Just find any beginners' reader on complex numbers, and watch the graphical representations, it should help you grok the way simple arithmetic applies to them.