An old chestnut here, and one that a few people have been badgering me to write about – this one’s for you, though, Linda B, since you’ve asked me to do it several times (because it bothers you, not because you don’t know the difference yourself, I hasten to add)
I think this one’s particularly difficult to grasp and remember because it is so often wrong – I think I really do see these two used incorrectly more often than I see them used correctly, which of course means it’s difficult to remember the correct way when you’re being bombarded with incorrect examples. Well, “bombarded” might be overdoing it, but there are lots of examples out there.
A compliment is an expression of praise or admiration, and to compliment someone is to praise or congratulate someone: “She complimented me on my new hat and I collected more compliments as I walked through the park”, “‘I love your dress’ – ‘Oh, this old thing? It’s nothing’ – ‘can’t you take a compliment?'”
A complement is a thing that contributes beneficial features or adds to something, and to complement is to contribute those extra features to it: “My writing skills are complemented by her marketing know-how”, “The green of the shoes complements the brown of the dress”.
Now, here’s the one people do really mix up …
Complimentary means expressing praise or admiration, as you would expect, given the definition and examples above. “Everyone was very complimentary about my hat”. But it also means free, without charge: “Please help yourself to the complimentary nuts on the bar.” I think this is how things get mixed up, because it seems like free things should be differentiated from things that are nice, so people think they need to go for the other spelling. But you don’t. Complimentary means supplied or given free of charge. Think of it this way: compliments are free!
Complementary, just to round things off, means combining with something else to make a complete whole or enhance each other. “Complementary colours” are those which look nice together in a design or outfit. It is used in the phrase “complementary medicine”, of course, too, which might make it easier to remember: complementary medicine complements or adds to conventional medicine to make a whole range of treatments you can choose from. So complementary medicine complements traditional medicine (it doesn’t tell it it looks great, it just supplements it and makes a better whole), and free things are complimentary.