In article <[EMAIL PROTECTED]>, Lawrence D'Oliveiro <[EMAIL PROTECTED]> wrote:
> In message <[EMAIL PROTECTED]>, Wildemar > Wildenburger wrote: > > > Tim Daneliuk wrote: > >> > >> One of the most common uses for Complex Numbers is in what are > >> called "vectors". In a vector, you have both an amount and > >> a *direction*. For example, I can say, "I threw 23 apples in the air > >> at a 45 degree angle". Complex Numbers let us encode both > >> the magnitude (23) and the direction (45 degrees) as a "number". > >> > > 1. Thats the most creative use for complex numbers I've ever seen. Or > > put differently: That's not what you would normally use complex numbers > > for. > > But that's how they're used in AC circuit theory, as a common example. Well, not really. They're often talked about as vectors, when people are being sloppy, but they really aren't. In the physical world, let's say I take out a compass, mark off a bearing of 045 (north-east), and walk in that direction at a speed of 5 MPH. That's a vector. The "north" and "east" components of the vector are both measuring fundamentally identical quantities, along perpendicular axes. I could pick any arbitrary direction to call 0 (magnetic north, true north, grid north, or for those into air navigation, the 000 VOR radial) and all that happens is I have to rotate my map. But, if I talk about complex impedance in an AC circuit, I'm measuring two fundamentally different things; resistance and reactance. One of these consumes power, the other doesn't. There is a real, physical, difference between these two things. When I talk about having a pole in the left-hand plane, it's critical that I'm talking about negative values for the real component. I can't just pick a different set of axis for my complex plane and expect things to still make sense. -- http://mail.python.org/mailman/listinfo/python-list