Complex refers to the amount of detail, components, steps, etc in a system. A complex problem may not necessarily be difficult. It might be an easy problem to understand but involve many different factors. Complicated refers to difficulty. Something can have few components but be very hard to understand. A difficult problem to solve. A complex system that (maybe!) isn't complicated is traffic light timing in cities. The problem isn't complicated to understand; you need to allow the traffic to flow as well as possible. You can just track traffic numbers to work it out. However there are many factors involved. Number of cars, rush hour, preferred routes, road works, school locations, accident likelihood, etc. The system is complex. My grandad thinks turning on our TV is complicated (it involves 3 buttons), but it definitely isn't complex.

Complex consists of many different and connected parts while complicated is someone or something that is hard to understand.

They are really similar and honestly some people might consider them interchangeable. But technically: Complex- there are a lot of aspects/components/parts to something, not NECESSARILY difficult (but 90% of the time it probably is) Complicated- something is difficult