You use complement to talk about making something complete, good, or effective. For example, if one food complements another, or is a complement to it, they go well together. If two people complement each other, they have personalities that are suited to each other.
1. As oregano comes from the Mediterranean, it is a perfect complement to aubergines and peppers.
2. Her interests and my interests complement each other: there is no conflict.
The ‘full complement’ of a group, set, or amount is every item or person that it normally includes or should include.
3. He lacks a full complement of teeth.
4. …a full complement of one thousand passengers and crew.
If you compliment someone, or pay them a compliment, you praise them or say something that shows admiration.
5. Thomas tried a smile, to compliment Mrs Jardino on her rough humour.
6. When he pays his compliment to you, show no reaction whatever.
7. Frank took the invitation as a great compliment.