Unawarebrah
Mugetsu Ookamiza
you pay attention to it, and if it involves stuff you're not familiar with and you don't mind reading check out some related topics. for example (just to pull something off the very top of my head since I'm sick today), reading up on philosophy a bit while watching Ergo Proxy or stuff about the monomyth and other mythic archetypes found around the world while watching Wolf's Rain.
What is a good entertaining "Complex" anime?
Would you say Darker than Black is considered one?
No, I would say that Darker then Black was a very disappointing anime, but there are people who would disagree with me on that. Hum I think that Detective Conan and most psychological and mystery based anime can how ever be very complex.
With shows like that you need to take your time and some times re-watch them or read about episodes to remind yourself of what happened.