So what exactly is a complex number?

[Tim Daneliuk]

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 ;)

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Tim Daneliuk     tundra at tundraware.com
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