What in the world are homophones? Homophones are words that share the same pronunciation but have different spellings--and different meanings. These pairs are different from homonyms, words that share the same spelling and pronunciation but have different meanings. "Compliment" and "complement" sound alike, but they different spellings and different meanings, so they are homophones. The word "tire" is a homonym--even though it is spelled the same way, it can mean a part of a car or bicycle, or it can mean fatigue. While you might not really care what these crazy things are called, you really should care about how a difference in spelling changes meaning.
Believe it or not, "compliment" and "complement" were originally used interchangeably. Over time, the two words have come to have two different definitions. I listed "compliment" first because it more commonly used. "Compliment" with an "i" is something nice you say to someone. For example, "I love your blog" is a compliment. The way I remember to use "compliment" when I write, "Thank you for that lovely compliment," is by thinking that I like to receive compliments, and there is an "i" in the correct choice.
"Complement" has to do with making something complete. My husband's willingness to do dishes complements my love of cooking. In other words, when we are in the kitchen together, our strengths allow us to complete the task. If you have a necklace or a tie that is especially effective with an outfit, it complements it. People also will write about a "full complement." For example, "Microsoft Office and Apple Works both offer a full complement of computer programs." If you are writing about things that complete, you need to use "complement," and complete has two "e's" in its spelling.
Did you notice that my explanation focuses on writing? When we talk, we don't need to think about the fact that there are two different spellings, but it is important to know the difference when you are writing because you want to make the best impression possible.
Again, here are my tricks: I like to receive compliments, but to complement is to make complete.
This blog on homophones is the first of a series. Do you have any demons that you would like me to slay? Leave a comment or send me a message, and I'll try to help.