Complement refers to something that makes something else perfect or complete. (not often used as a noun)
Compliment refers to saying something nice or praising, such as you look nice this evening.
Complement means “to complete, to provide something lacking, or form a complement to.”
That hat really complements your dress.
Compliment means to praise, congratulate, or say something admiring to someone.
They complimented her on her new job.