Complement(ary) vs. Compliment(ary)How to use "complement" and "compliment" correctly
The verb complement means “to complete; to fill out by supplying what something else lacks.” Remember this by relating it to the use of the term complementary in math: it describes two acute angles that together form a right angle.
They were a good team because her technical skills complimented his creativity.
They were a good team because her technical skills complemented his creativity.
They were a good team because their talents were complementary.
One meaning of complimentary is “free of charge”:
complimentary beverages on the flight
A compliment is an expression of praise; as a verb, to compliment means “to express praise.” Therefore, complimentary can also mean “expressing praise”:
Give my compliments to the chef.
highly complimentary review of the restaurant
Common Errors in English Usage: Errors in diction and idiom commonly made by native speakers of English
List of Common Errors in English Usage (PDF): Printable version of the complete list
Common Grammar Errors: A list of common errors in grammar (topics like subject-verb agreement and parallelism) as distinct from usage