Your answer is quite similar to the one I got from a college math professor when I asked about i. He said it doesn't sound like it makes sense but it makes possible a number of elegant proofs and has practical applications.

I still don't understand how -1 can have a square root given that a positive number times itself yields a positive result and a negative number times iteslf yields a positive result. So exactly what numbers can be multiplied by themselves to give negative results? (Yeah, I know: i).

Mike