Christophe's answer is correct, but I think that the meaning of these two words is so similar that usually they are just used interchangeably. I.E. they can generally be used as if there is no difference.

The difference is very small. Both mean "not simple". So it means there are alot of parts, and details. But "complicated" means challenging, difficult to understand. "Complex" is closer to "highly evolved". In short, complicated is negative, complex is neither negative nor positive. This Mathematics problem is very complex. Its too complicated for a beginner.