Words having similar spelling cause confusion but having identical pronunciation makes things more difficult. This is the case with the terms complement and compliment.
When used as a noun, the term complement denotes “a thing that completes or brings to perfection” or “a number or quantity of something required to make a group complete.”
“Philip’s wireless light is a perfect complement to the company’s popular Hue bulbs”
Business Insider“The Best Complement? Completing Each Other”
Chabad.org“It’s Not a Complement”
America Magazine
Complement as a verb means “to add to something in a way that enhances or improves it or makes it perfect.”
“What Does It Take For A COO to Complement an Entrepreneur”
Entrepreneur.com“Talented juniors complement seniors”
NorthJersey“Fiscal policy needs to complement monetary steps-ECB’s Nowotny”
Reuters
Meanwhile, compliment, when used as a noun, refers to “a polite expression of praise or admiration.”
“When Does A Compliment Become Sexual Harassment?”
Huffington Post UK“Knicks’ Carmelo Anthony gives Jeremy Lin backhand compliment, says he is ‘excited’ for Nets point guard”
New York Daily News“Asking for Money? Compliment the Donor, Not Your Organization”
New York Times
Compliment may also be used as a verb meaning “to politely congratulate or praise someone for something.”
“What happened when Trump and Clinton were forced to compliment each other”
Washington Post“Student racially abused after complimenting woman on her dog”
Metro“Tap This: Good meals compliment good beers”
The Weekender
Another source of confusion is their adjective forms complementary and complimentary. The adjective complementary means “combining in such a way as to enhance or emphasize the qualities of each other or another.”
“After cancer treatment, complementary care calms”
USA TODAY“Steel giants hit by losses see hope in complementary businesses”
China Daily“Complementary and Alternative Medicine: What Works?”
MD Magazine
On the other hand, complimentary refers to “expressing a compliment; praising or approving” or “given or supplied free of charge.”
“Morning Sports Update: Bills aren’t overly complimentary of Rob Gronkowski”
Boston Daily“British Airways offers complimentary one-way first class upgrade”
Business Traveller“Metquarter is offering complimentary cut throat shaves”
Liverpool Echo
There is a simple trick to remembering the difference of these two terms: If you are talking about completeness, then you must use complement, but if you are referring to giving praise or approval, you must select compliment.