# So what exactly is a complex number?

Wildemar Wildenburger lasses_weil at klapptsowieso.net
Sat Sep 1 11:22:28 CEST 2007

```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

```