On Nov 20, 2007 5:39 PM, Frank Barknecht fbar@footils.org wrote:
For some calculations polar, for others cartesian coordinates are easier to use. To quote Miller:
The main reason we use complex numbers in electronic music is because they magically automate trigonometric calculations. We frequently have to add angles together in order to talk about the changing phase of an audio signal as time progresses (or as it is shifted in time, as in this chapter). It turns out that, if you multiply two complex numbers, the argument of the product is the sum of the arguments of the two factors.
I still don't exactly understand why one couldn't just use (x, y) vectors; why the y value has to be multiplied by something imaginary. I mean, i/j is *defined as* the square root of -1, but it can't really *be* the square root of -1... I've accepted it and moved on to more practical questions, but that is still mysterious for me.