Complete : is when you finish something. (like an activity or something. Complement : contribute extra features to (someone or something) in such a way as to improve or emphasize their qualities.

Complete : is when you finish any activity you were doing. Complement : Is to Improve or Emphasize, to add an extra feature on what you were doing.

You will complete your task in half an hour. (complete=finish) Complement (as a noun) is often called 'charming lie'.