Compliment v. Complement
It is so easy to get these two mixed up. Most people don’t even realize there are two. And the words are used more in conversation than in writing, so you can’t tell which one is being used.
We’re most familiar with compliment. “You did that very well.” “ I love your bag!” “You have great understanding.”
When you are referring to some sort of completion, the term is complement. Let’s say you’re on a committee with two other people and you all have different strengths that your project needs. You would say you complement each other. If you have a complete set of something, you could be said to have a full complement of whatever it is. That’s one way to know when to use which word: Just look at the way the word is spelled. Compliment would not refer to complete, which is spelled with an e, not an i, so you would use the term that has the e.
Another way to remember is that a compliment is about you. Or I. Which is grammatically wrong – it would be me – but works as a pneumonic.