compliment · noun /ˈkɑm.plə.mənt/Full view
compliment
C2 C something that you say or do to show praise or admiration for someone
Dictionary example:

Thank you for the compliment, but many people helped me along the way.

Learner example:

I take that as a compliment, giving me hope to excel as well as he did. (Certificate of Proficiency in English; C2; German)

pay sb a compliment
C2 to tell someone that you admire something about them
Dictionary example:

He paid her several compliments about her painting.

Learner example:

His companions always pay him compliments on his [piano] playing. (Certificate of Proficiency in English; C2; Polish)

with the compliments of sb
C2 used by someone to express good wishes when they give you something free, for example in a restaurant
Dictionary example:

Please accept this champagne with the compliments of the manager.

Learner example:

The guest can also choose from a selection of wonderful desserts such as mousse au chocolat with fresh ras[p]berries before finishing his/her meal with a rose lique[u]r - with the compliments of the house (and the bill). (Certificate of Proficiency in English; C2; German)

compliment · verb T /ˈkɑm.plə.ment/
compliment
C1 to praise or express admiration for someone
Dictionary example:

He complimented me on my writing.

Learner example:

Firstly, I must compliment you on lowering your prices and adding new destinations to choose from. (Certificate in Advanced English; C1; Slovene)

Cambridge logo