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So what exactly is a complex number?

Wildemar Wildenburger lasses_weil at klapptsowieso.net
Fri Aug 31 18:52:23 EDT 2007 
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
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