So what exactly is a complex number?

[Lawrence D'Oliveiro]

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.