complexadjective |kämˈpleks; kəmˈpleks; ˈkämˌpleks|1 consisting of many different and connected parts : a complex network of water channels.• not easy to analyze or understand; complicated or intricate : a complex personality | the situation is morecomplex than it appears.
complicated |ˈkämpləˌkātid|adjective1 consisting of many interconnecting parts or elements; intricate : a complicated stereo system.• involving many different and confusing aspects : a long and complicated saga.
While the two words seem for most part interchangeable, to me complicated always has a negative connotation complex doesn't. As in:
A: How's your love life?
B: It's complicated.
When I read a review praising a film or book as complicated my inner pedant winces and reaches for the red pen.