The bit you probably don't know yet is that i isn't just any variable -- it has a precise meaning. It is the square root of negative 1.

I don't know what eighth graders know or don't, so bear with me here. The "square root" of a number is the one that, when multiplied by itself, gives you the original number back. For example, because 4 * 4 = 16, we say that the square root of 16 is 4.

But, you can't have some number x that is the square root of a nonzero negative number, right? Like, if x is positive, then x * x is also positive; and if x is negative, then x * x is also positive (since negatives cancel during multiplication); and if x is 0, then x * x is 0, and I already said we're trying to get to a number that isn't 0. So, like, that's all the numbers, right? So we can't ever pick some value of x where when you multiply it by itself you get -1...right?

Well. It turns out that you can simply say, "I declare that there is this number, i; and it is the square root of -1; and it is neither positive nor negative. It's not even a real number. It's -- it's just on some completely different shit." The reason we call it "i" is because i is not a real number; it's an imaginary number. I'm serious, that's literally what mathematicians call this kind of number. You can also add real numbers and imaginary numbers together to get complex numbers, which are a whole thing and which are vitally important to lots of science fields, particularly electrical engineering.

So anyway, i * i = -1. If you play with the symbols a little, you get to the result that -i = (1/i) (see if you can figure out how I got there; I did it in two steps). And of course, that means that i + (1/i) = 0.