To pay a compliment is to say something in praise of somebody, out loud, to their face. Nice haircut. That was a good piece of work.
The same money metaphor as paying attention, and it takes to: he paid one to the cook. A backhanded compliment has an insult folded into it, and fishing for compliments is angling to be paid one. Watch the spelling against complement, which is the thing that completes something else and has nothing to do with praise.
1phrasepay a complimentTo say something in praise of somebody.
“It costs nothing to pay a compliment.”
pay a compliment is an act of praise.
Practised in Common Word Pairs