com·pli·ment 
(kŏmplə-mənt)
(kŏmplə-mənt)n.
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.
[French, from Italian complimento, from Spanish cumplimiento, from cumplir, to complete, from Latin complēre, to fill up : com-, intensive pref.; see COM- + plēre, to fill; see pelə-1 in the Appendix of Indo-European roots.]