Complex numbers are seldom used in daily life, altough you could say that every real number is complex, but with the imaginary part equal to zero. And btw. "complex" is a bit of a misnomer, perhaps we should call them "easies", because often they make it easier to perform certain math tasks.
It all started in Italy, 13th century or so when mathematicians where trying to solve quadratic and cubic equations. Here is my solution in C# of the cubic. I used the rules found in wikipedia.
Included a zip file with a small formsapplication that exercises the method given here.