The duke was most complimentary about my sculpture.
2 free, gratis, on the house:
The shoehorn is complimentary when you buy a pair of shoes.
Advanced English Dictionary
+adjective 1 given free of charge: complimentary tickets for the show 2 ~ (about sth) expressing admiration, praise, etc: a complimentary remark + She was extremely complimentary about his work. Compare: UNCOMPLIMENTARY - COMPLIMENT
Collocation Dictionary adj
extremely, highly, very
She made some highly complimentary remarks about their school.
Random quote: To be beautiful means to be yourself. You don't need to be accepted by others. You need to accept yourself.: Thich Nhat Hanh