Here’s a trick to help you figure out which spelling you need. Complement, which means to complete, has the same first six letters as complete. Knowing that I should say nice things to people more often will help me remember that compliment has an i.
Monday Muddle: compliment, complement
compliment: (noun) an expression of praise, admiration or appreciation;(verb) to give a compliment complement: (noun) something that completes, makes whole, or brings to perfection; (verb) to complete, make whole, or bring to perfection