Max2009 wrote:I hate complex numbers. I mean, calculus was hard enough to begin with, why the hell did they have to go and invent imaginary numbers? Were they deprived of imaginary friends as children and now want to get back at the rest of the world?
Amazingly enough, calculus actually gets easier
when you introduce complex numbers. Trying to do calculus on functions of two or more real variables quickly becomes a real pain in the neck, but if you can use a complex function instead, things become much simpler. You don't have to worry about such things as curl, divergence, the del operator, or any of that other stuff - if the function has "is analytic" and has a derivative at all, you can find it the same way you find derivatives of real functions. And analytic functions have all sorts of other properties that make them easier to work with, too.
Also, to answer your other question, imaginary numbers were invented in order to solve cubic
equations - when you plug numbers into the cubic formula, you sometimes end up having to deal with imaginary terms in the process of getting your answer, even if all three roots are real.