As some of you may know, I study Latin. I'm not that good at it, but study Latin I do. Anyway, the language is complex - each noun has five (occasionally six) declension, each verb has about 36 different forms, and so forth.
Latin is very elaborate. As a result, it is worse (in certain respects) than modern English. English is not as hard to learn, and can easily absorb technical and foreign words. Over time, Latin degenerated into more handy, convenient versions such as French and Spanish, which are approximately as complex as English. Language thus has evolved from complex to simple, rather than the other way around.
Then again, Latin is rather simple. It gives each word the fewest number of meanings possible - "domi," for instance, only means "at home" - and has standard rules for every situation. In contrast, the English language uses a bunch of prepositions and very few suffixes, making it necessary to guess a word's meaning from the context of the sentence it is in. (For instance, the "it" I just used. Is "it" a word, a meaning, a guess, a necessity? You have to figure out.)
So Latin is more complex than English, since there are so many rules, but more simple, since those rules are more universally applied. What practical use this can be put to, I leave to someone with more time.