If someone pays you a complement you should be confused rather than flattered. Likewise, your scarf probably doesn’t compliment your outfit (unless you have a talking scarf). Here’s why:
To complement something means to complete or supplement something. To compliment is to praise something. So, that red wine might complement the meal, but if it compliments the meal, you’ve drunk too much.
The same differences hold true for the words complimentary and complementary. In this case, something that is complimentary is either flattering or given freely: a complimentary breakfast at the hotel or a complimentary note from a secret admirer. Something that is complementary completes or supplements something: the countertop was done in a complementary color or the waitress provided complementary cream and sugar for my coffee.
One small letter separates these words, and while that one letter may not make much of a difference in everyday use, you can bet that the test designers who craft verbal tests (like the SAT) will count on that one letter to trip you up.
Just remember: Something that complements completes (look at the “e” in “complete”) and something that compliments praises (look at the “i” in “praise”).
Originally Posted on C2 Education Blog