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.


Oh, one other thing I neglected to mention.  My use of "vector" here
is certainly incorrect in the mathematician's sense.  But I first
ran into complex arithmetic when learning to fly an airplane.
The airplane in flight has a speed (magnitude) and a bearing (direction).
The winds aloft also have speed and bearing.  These are called
the aircraft "vector" and the wind "vector" respectively.  They must
be added to compute the actual (effective) speed/direction the aircraft
is flying.  In the Olden Days (tm), we did this graphically on a
plastic flight computer and a grease pencil.  With the advent of
calculators like the HP 45 that could do polar <-> rectangular
conversion, this sort of problem became a snap to do.  It is from
this experience that I used the (non-mathematical) sense of the
word "vector" ...

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Tim Daneliuk     tundra at tundraware.com
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