Language usage complaint of the day.

Complement and compliment have different meanings and even a slight difference in pronunciation. ( a short 'i' in compliment, a long 'e' in complement)
See the following dictionary information.
compliment[French, from Italian complimento, from Spanish cumplimiento, from cumplir, to complete, from Latin complre, to fill up : com-, intensive pref.; see com- + plre, to fill]
noun: com-pli-ment
1. An expression of praise, admiration, or congratulation.
2. A formal act of civility, courtesy, or respect.
3. compliments Good wishes; regards: Extend my compliments to your parents. See Usage Note at complement.
tr.v. com-pli-ment-ed, com-pli-ment-ing, com-pli-ments
1. To pay a compliment to.
2. To show fondness, regard, or respect for by giving a gift or performing a favor.