So what exactly is a complex number?

[Grzegorz Słodkowicz]

> Here is a simple explanation (and it is not complete by a long shot).
>
> 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".
>
> 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.
>
> Complex Numbers show up all over the place in engineering and
> science problems.  Languages like Python that have Complex Numbers
> as a first class data type allow you do to *arithmetic* on them
> (add, subtract, etc.).  This makes Python very useful when solving
> problems for engineering, science, navigation, and so forth.
>
>
> HTH,
>   
You're mixing definition with application. You didn't say a word about 
what complex numbers are, not a word about the imaginary unit, where 
does it come from, why is it 'imaginary' etc.  Since we're being arses 
here I'd hazard a guess you were educated in the USA where doing without 
understanding has been mastered by teachers and students alike. You're 
explanation of what vectors are is equally bogus but this has already 
been pointed out. I'd also like to see a three-dimensional vector 
represented by a complex number.

Besides, I find Wikipedia extremely unhelpful for learning maths, partly 
beacuse of it's non-linear nature (while reading an article you come 
across a term you don't know, follow a link, then follow three others 
and over the next 4 hours you find out lots of interesting things which 
are sadly at best tangential to the initial subject) and because it's 
written by people who already know a lot about the subject and take many 
things for granted. This seems to be a decent introduction: 
http://www.ping.be/~ping1339/complget.htm

Regards,
Greg