Two soundalike words that are frequently mistaken for one another in written form are "compliment" and "complement." Often, compliment is used when what is meant is complement.
Compliment, which can be used as either a noun or a verb, means praise. One can either compliment someone or give someone a compliment. Examples: "I would like to compliment you on your attire." "I must compliment her dress." "He gave me such a nice compliment abuot my hairstyle."
In addition, if something is free of charge, we often refer to it as "complimentary." Examples: "Admission to the ball game is complimentary on Sunday." "The restaurant owner served me a complimentary bowl of soup."
Complement is a term that refers to completing or supplementing and can also be used as either a noun or a verb. An easy way to remember its spelling is to think of the word "complete," which is a reminder to use an "e" rather than an "i." Examples: "The dessert you brought is a perfect complement to the main course." "His talent as a pianist complements my skills as a singer."
Essentially, if you're not praising someone or something, or referring to something that's free of charge, the word you want to write is "complement."
Incorrect: "Your new carpet is a perfect compliment to the furniture."
Correct: "Your new carpet is a perfect complement to the furniture."
Correct: "I would like to compliment your beautiful new carpet."