complexity vs difficulty

complexity

noun
  • That which is and renders complex; intricacy; complication. 

  • The state of being complex; intricacy; entanglement. 

difficulty

noun
  • That which cannot be easily understood or believed. 

  • Physical danger from the environment, especially with risk of drowning 

  • An obstacle that hinders achievement of a goal. 

  • The state of being difficult, or hard to do. 

  • An objection. 

  • An awkward situation or quarrel. 

How often have the words complexity and difficulty occurred in a corpus of books? (source: Google Ngram Viewer )