Hallo, Chuckk Hubbard hat gesagt: // Chuckk Hubbard wrote:
That's just it, it's convenient.
Convenience is very important in math. For example, in some geometric problems it's more convenient to work with polar coordinates instead of cartesian. A large part of math (and all other sciences, too) consists of finding simpler methods and explanations than you had before (while still staying "correct").
The motivation to introduce complex numbers and that funky imaginary unit i (or j in DSP books) is, well, complex. For a detailed introduction you might want to review somehting like that: http://en.wikibooks.org/wiki/Algebra:Complex_numbers Especially the part with the geometric interpretation and Euler's formula is useful to understand some of the motivation.
Another nice and short introduction I found is this: http://www.physics.umd.edu/courses/Phys374/fall04/files/ComplexNumbers.pdf
It's written for physicists, so it's a bit dumbed down to be more hands-on. ;) (I'm allowed to say this as I studied physics myself.)
Ciao
Frank Barknecht _ ______footils.org_ __goto10.org__