Difficulty: Moderately Easy
Step1
Write "compliment" when you're talking about saying something nice. The word "compliment," with an "i," is both the verb for sweet-talking someone and the noun that is the sweet talk itself. You compliment someone when you give them a compliment like "Gosh, I really admire the way you use 'compliment' correctly!"
Step2
Use "complement" when you're talking about things that complete each other or go well together. "Complement," with an "e," is also both a verb and a noun. So you complement your outfit by choosing a matching hat, and your matching hat is a complement to your outfit—which may earn you a compliment. To make things even more complicated, a "complement" is also a complete set of something, as in, "This article certainly has a full complement of homophones."
Step3
Move on to adjectives very carefully. Both "compliment" and "complement" can take the form of adjectives, and most of the time they follow the meaning of the verb and noun—but not always. A complimentary note, for example, can be a letter full of praise for that great dinner party you gave. But "complimentary" can also mean "free of charge," so your complimentary note may just be a piece of stationery someone's giving away.
Step4
Remember that math is another thing altogether. The adjective "complementary" usually means completing or filling out or matching, as in "He assembled the complementary parts of the entertainment center." But in the world of math, "complementary" describes two angles that add up to 90 degrees, as in "Once he tried to put the shelves in, however, he found that the entertainment center's walls didn't meet at a complementary angle."
Step5
Play it safe by never writing these words down. Since "compliment" and "complement" are homophones, you can use them incorrectly in spoken communication all you want, and no one will know the difference. As a matter of fact, the difference didn't exist in most usage books until relatively recently; both spellings were used interchangeably. When you're struggling to write your next complement of prose, then, you probably won't want to compliment the persnickety grammarian who decided to complicate your life.
