This is so the wrong place for this discussion

Being a scientist myself, we don't care if the number is real or not, complex numbers are just a way to make 2D calculations easier to spell out. Then when you want to go 3D, 4D, ... 3x3D etc... tensor calculus comes to play. And still nobody cares if the numbers are real or not. It's just an aggreement to make the syntax look clearer.

To easily understand the basic operations of complex and real numbers, have a look at the geometric interpretation:
http://en.wikipedia.org/wiki/Complex_number