Fractal Theory: Imaginary Numbers
But first, a quick refresher math course.
We should all remember that the square root of nine is three, of four is two, and of one is one. But how many remember what the square root of negative one is? (Those who said "me" can skip to the next paragraph. Those of us who once knew but have somehow forgotten should probably read on.) Well one answer to what is the square root of -1 is that there isn't one. However another answer, which is equally valid, and perhaps far more interesting, is that because there isn't any number which multiplied by itself gives us -1, we'll create one. That's a handy way of plugging up all sorts of mathematical theories that would otherwise have special cases for when you need the square root of a negative number. How do we "create" a number which is the square root of -1? Simple. Just get enough mathematicians together in one room and get them to all agree that from then on, the letter "i" represents the square root of -1. That's all it takes. That's all it took. A convention of mathemeticians creates the convention of "i," and "i" is subsequently recognized as being the square root of -1.
So, if "i" is the square root of negative one, then two times "i" is the square root of negative four, three times "i" is the square root of negative nine, etc. All these numbers that are multiplied by "i" are called imaginary numbers, a throwback to those early years when mathematicians weren't quite sure whether they were real or not. Numbers that aren't multiplied by "i", regular numbers, are called real numbers. Simple enough.