So what exactly is a complex number?

Tim Daneliuk tundra at
Sun Sep 2 04:26:11 CEST 2007

Wildemar Wildenburger wrote:
> Lawrence D'Oliveiro wrote:
>> In message <46d89ba9$0$30380$9b4e6d93 at>, 
>> 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 

It was badly stated, I'll agree.  What I should have said is something
like "An apple is launched at 45 degrees." thereby sticking to the
magnitude and direction thing.

> at 16 degrees to 4 apples at 25 degrees and the result making any sense.

No, but go to my other example of an aircraft in flight and winds
aloft.  It is exactly the case that complex numbers provide a convenient
way to add these two "vectors" (don't wince, please) to provide the
effective speed and direction of the aircraft.  Numerous such examples
abound in physics, circuit analysis, the analysis of rotating machinery,

> Anyway, that was just humorous nitpicking on my side, don't take it too 
> seriously :).

I didn't and I concede I could have provided a better and crisper example.

> /W

Tim Daneliuk     tundra at
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