complementary adj. completing something or satisfying a lack in something.
complimentary adj. 1. flattering; expressing praise. 2. given freely and without cost.
Words in the Wild: After she left her complimentary remarks about the concierge with the hotel manager, Sonja found complimentary scones outside her door each morning with complementary clotted cream and jam.
This lexical vexation often finds its way into writing, but it’s pretty easy to check for once you know to be on the lookout. Complementary has the e from complete, and complimentary has the i from compliment.
Still vexed? You can find a complete list of the Word Blog’s lexical vexations here.