To complement a compliment…
Did you know that compliment is not the same as complement? They actually have quite different meanings so using the wrong word can make a reasonable sentence into nonsense!
compliment - expression of praise, greeting, positive comments
She complimented the floral arrangement on the table.
complement - to complete or make a whole
The new couch complements the room nicely.
Can you see how complete complementary things are as a reminder for which spelling to use?