Complement vs Compliment
Quick answer: A complement (with an E) completes something — colors that complement each other. A compliment (with an I) is kind words of praise.
Complement
Noun/verb: something that completes or pairs well with another.
“The sauce complements the fish perfectly.”
Compliment
Noun/verb: an expression of praise.
“She complimented my presentation.”
How to remember it
complEment complEtes; complIment = 'I like it.'
Common mistake
'My complements to the chef' — praise takes the I.