Like many math newbies, complex numbers (or at least the idea of complex numbers) are a source of some confusion... but I've worked with them before and I'm reading through posts on PF that I hope will give me some sense of intuition about them. That said, there is one nagging question that I've never seen addressed -- what value does a calculator use for i? If e^(i)(pi) is equal to -1, and e^pi is equal to 23.14069263~, it seems (to my inexperienced mind) that there'd have to be a more concrete value to i than some number that, when squared, gives -1 -- at least when it comes to computations done by a programmed machine. Naturally when I tried to solve it with logs, dividing ln(-1) by ln(pi) my calculator said it was a nonreal number... which I was expecting given that I was attempting to solve for i. Any thoughts? I'm aware that this is probably an incredibly naive question.. I'm just hoping that the answer is something other than "Calculators use some number that, when squared, is equal to -1." xD Calculators are programmed by humans so I'm guessing there should be some value for i programmed into it -- what is the "some number" value used by a calculator when it deals with complex numbers?