Wildemar Wildenburger <(E-Mail Removed)> wrote:

> Again, that is just one way to interpret them. Complex numbers are not

> vectors (at least no moe than real numbers are).
OK, let me take a shot at this.

Math folks like to group numbers into sets. One of the most common sets is

the set of integers. I'm not sure what the formal definition of an integer

is, but I expect you know what they are: 0, 1, 2, 3, 4, etc, plus the

negative versions of these: -1, -2, -3, etc.

The set of integers have a few interesting properties. For example, any

integer plus any other integer gives you another integer. Math geeks would

say that as, "The set of integers is closed under addition".

Likewise for subtraction; any integer subtracted from any other integer

gives you another integers. Thus, the set of integers is closed under

subtraction as well. And multiplication. But, division is a bit funky.

Some integers divided by some integers give you integers (i.e. 6 / 2 = 3),

but some done (i.e. 5 / 2 = 2.5).

So, now we need another kind of number, which we call reals (please, no nit

picking about rationals). Reals are cool. Not only are the closed under

addition, subtraction, and multiplication, but division too. Any real

number divided by any other real number gives another real number.

But, it's not closed over *every* possible operation. For example, square

root. If you take the square root of 4.23, you get some real number. But,

if you try to take the square root of a negative number, you can't do it.

There is no real number which, when you square it, gives you (to use the

cannonical example), -1. That's where imaginary numbers come in. The math

geeks invented a wonderful magic number called i (or sometimes j), which

gives you -1 when you square it.

So, the next step is to take an imaginary number and add it to a real

number. Now you've got a complex number. There's all kinds of wonderful

things you can do with complex numbers, but this posting is long enough

already