Wildemar Wildenburger wrote: > Tim Daneliuk wrote: >> A number by itself is called a "scalar". For example, when I say, >> "I have 23 apples", the "23" is a scalar that just represents an >> amount in this case. >> >> 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. > 2. Just to confuse the issue: While complex numbers can be represented > as 2-dimensional vectors, they are usually considered scalars as well > (since they form a field just as real numbers do). > > >> There are actually two ways to represent Complex Numbers. >> One is called the "rectangular" form, the other the "polar" >> form, but both do the same thing - they encode a vector. >> > Again, that is just one way to interpret them. Complex numbers are not > vectors (at least no moe than real numbers are). > > > /W
Yeah, I know it's a simplification - perhaps even a vast simplification - but one eats the elephant a bite at a time. FWIW, the aforementioned was my first entre' into complex arithmetic, long before I waded through complex analysis and all the more esoteric stuff later in school. I wonder why you think it is "creative", though. Most every engineer I've ever know (myself included) was first exposed to complex numbers in much this way. Then again, I was never smart enough to be a pure mathematician ;) -- ---------------------------------------------------------------------------- Tim Daneliuk [EMAIL PROTECTED] PGP Key: http://www.tundraware.com/PGP/ -- http://mail.python.org/mailman/listinfo/python-list