Don’t confuse the words “compliment” and “complement.”
“Compliment” can be a noun or a verb. As a noun, it means a flattering remark: She always receives lots of compliments when she wears that beautiful dress. As a verb, it means to give a compliment: Bryan complimented Carol on her new hairdo.
“Complement” can also be a noun or a verb. As a noun, it means something that completes or improves something else: Gravy is the perfect complement to mashed potatoes. As a verb, it means to complete or to improve: The players’ styles complemented each other nicely.
It may help to picture the word “complement” as “comple(te)ment.”