Sometimes people get confused when they use the words “complement” and “compliment.” Complement (with an “E” in the middle) means something else that makes an item complete (note the “E” there, too.) Just think of the movie Jerry Maguire, in which Tom Cruise told Renee Zellweger: “You complete me.” Thus, she was his complement. And yes, I’m sure she accepted his statement as a compliment (with an “I” in the middle), which means praise or respect.
Here’s how we can remember this: “Woman was created as a complement of man, but if the man wants to stay in her good graces, he needs to learn how to compliment her — and often!”
And this short grammar lesson is complimentary, which means “I” gave it to you free of charge.