So what exactly is a complex number?

Tim Daneliuk tundra at
Fri Aug 31 19:53:13 CEST 2007

Carsten Haese wrote:
> On Thu, 2007-08-30 at 20:11 -0500, Lamonte Harris wrote:
>> Like in math where you put letters that represent numbers for place
>> holders to try to find the answer type complex numbers?
> Is English your native language? I'm having a hard time decoding your
> question.

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.

Tim Daneliuk     tundra at
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