So what exactly is a complex number?

[Tim Couper]

.. FWIW the fundamental difference in using complex number to represent 
purely vector information is that the algebra of complex numbers is such 
that the product of two of the imaginary components has a result in the 
real range (and a product of a real and imaginary components is in the 
imaginary range, etc); so what you are modelling should have this 
behaviour if you're using complex numbers to represent it;  otherwise a 
vector representation could be more appropriate. So in areas of physics 
where complex number representations are used, rather than vector, it's 
because this this algebra *is* appropriate. Now, if you're modelling 
entities that has up to 2 numeric components, which dos not have this 
"complex number" behaviour, and you're at most going to add and subtract 
these, then the representation of this as vector or complex number model 
are indeed identical. This could, however, be considered a special, or 
at least a simple, case.

Dr Tim Couper
CTO, SciVisum Ltd

www.scivisum.com



Wildemar Wildenburger wrote:
> Lawrence D'Oliveiro wrote:
>   
>> In message <46d89ba9$0$30380$9b4e6d93 at newsspool4.arcor-online.net>, 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.
>>     
>  >
> OK, I didn't put that in the right context, I guess. The "magnitude and 
> direction" thing is fine, I just scratched my head at the "23 apples at 
> 45 degrees" example. Basically because I see no way of adding 2 apples 
> at 16 degrees to 4 apples at 25 degrees and the result making any sense.
> Anyway, that was just humorous nitpicking on my side, don't take it too 
> seriously :).
>
> /W
>