Complement and Compliment are two different words. Armed with this knowledge, you are now better at English than, in my approximation, roughly 100% of stores, hotels, airlines, et cetera.
Let’s dive deeper.
Complement. The word Complement concerns things that fit together. For example, if your choice of wine really brings out the meatiness of your meaty foods, the wine complements the meal (assuming you are the kind of person who enjoys the flavour of wine, and you’re not like me and consider it the taste of the bitter agony of grapes’ rotting corpses). If you received said wine on the house, it was complementary. This is where everybody goes wrong – I dare you to find an example of a free bonus being called complementary like literally anywhere ever.
Compliment. I’m sure you know this one already, since this is the word whose existence people in general are aware of. It’s saying nice things, so for example “Wow, author of this post, you sure do understand English better than most actual native English speakers” would be a compliment (also aw shucks stop it you).
For one last example, imagine I hand you a free bag. On this bag is printed the phrase “You are a fabulous human being”. This bag is both complementary and complimentary.
Now go forth, enjoy your newfound smug superiority, and I’m sorry about how you can never look at a store’s homepage again without getting annoyed that they got it wrong.
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