According to the dictionary definitions, "complex" and "complicated" almost always can interchange when it comes to "difficulties" that you deal with in a situation or problem. Consequently, it should come as no surprise that the two nouns "complexity" and "complication" should also be nearly the same things. But perhaps they are not!
- The state of having many parts and being difficult to understand or find an answer to.
- Something that makes a situation more difficult.
To elaborate my meaning, I would like to raise two examples here:
- The complexity of urban life is increasing day to day.
Ngram shows that, the word "complication" cannot be substituted for "complexity" in this sense or it is used very rarely.
For more clarification, let me bring up another example:
- The complexities of human relationships have become a quite significant and serious issue today.
Again, Ngram reveals that these two cannot be replaced or at least "complication" is not used much in this sense.
Now, I wonder if it is a matter of formality where Ngram cannot look up informal cases, or it is a matter of fixed phrases? Please do me a favor and help me with this question.