>>Where advanced math lost me was i. The square root of -1. Riddle me that, joker. I had a long discussion with a math prof -- not Alexandra Bellow, sadly -- who said I know it doesn't seem to make sense, but it makes possible a great number of elegant proofs. Oh. Kay.
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>The idea of a number, or of a set, doesn't necessarily make sense - they're both equally abstract. But any half decent math teacher can give you examples where these can apply.
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>The whole point of (the art of) abstract thinking is that you shouldn't need examples. Speaking in OOP, i is a class with a some properties (i.e. its definition as sqrt(-1)) and then the events and methods follow logically. Then you have a general complex number, which is basically a binome (can't get myself to say "binomial" because I'd immediately ask "a binomial what?"), with which you then calculate with just like any other binome. Don't like the properties? Surprised with what you get? So what? It is so.
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>I also thought that complex numbers had no practical use short of aerodynamics (there's a function in the form of y=(az+b)/(cz+d), named after Zhukovsky or some other Russian airplane builder - it describes the flow of air around the wing), but then when I was teaching in a vo-tech school an engineer who taught the electric technicians said I should push the guys with complex numbers... because if you express capacitance as the real component, and inductivity as the imaginary, the whole impedance thing becomes quite clear and the kids actually like it because it finally starts making sense. Go figure :).

Your understanding of advanced math is clearly beyond mine. My understanding of "i" never got past the basic definition: the square root of -1. Given that a positive squared is a positive, and a negative squared is a positive, what squared gives you a negative?

Well, yes, an imaginary number. I don't like imaginary numbers.