Introduction
Complex numbers are easy to work with if you know some of the basic concepts. Complex numbers were invented/discovered so that we can perform some of the calculations that require taking the square root of a negative number.
In a more specific application, I think as computer and electrical engineers, we use complex numbers to make our calculations for circuits a little bit simpler. Instead of using V and I to describe a circuit, we simply use Z, the impedance, which has a real and complex part.
Quick Terminology
Many examples use $ i $ as the basis for complex numbers, but as engineers we like to be cooler, so we use $ j $.
$ j=\sqrt-1 $
$ j^2=-1 $
Examples
$ (10j)(3j)=(10)(3)(j)(j)=(30)(j^2)=(30)(-1)=-30 $
$ (-4j)(20j^2)(-3j)(j)=(-4*20*-3*1)(j^5)=(240)(j)=240j $
Sources
http://www.purplemath.com/modules/complex.htm
http://www.math.toronto.edu/mathnet/questionCorner/complexinlife.html
