So what exactly is a complex number?

[Boris Borcic]

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?
> 

Not quite. Relating them to (plane) trigonometry is much closer to the mark. 
Complex numbers are like a subclass of real numbers that elegantly extends the 
usual arithmetic operations to provide access to trigonometric functions and 
related goodies. This then allows you to think of trigonometric problems as 
simple arithmetic problems.