Hi Jou, These two words are certainly different in their meanings. When we "compliment" someone or "pay someone a compliment", we praise them for an admirable quality which they possess. Examples: She complimented Andy for his inspiring speech. / I would like to pay you a compliment for your bravery. When two things "complement" each other, they enhance each other's quality. Examples: His blazer complements his white oxford shirt. / French fries and ketchup complement each other. In your question, someone is asking if something (which I presume to be a piece of clothing or a fashion accessory) makes him or her look better. Under this context, "complement" should be chosen as the appearance of a person is enhanced. Just as a side discussion, look at the following sentence: Mary's new pearl necklace really complements her floral blouse perfectly. When I saw her this morning, I complimented (praised) her for her impeccable taste. Hope this helps. Cheers