The words complimentary and complementary are very easy to confuse. One means 'To praise' or 'Offered freely,' the other means 'To complete.' Here are some usage examples you won't find in the dictionary...

Complementary colour - One of a particular pair of colours whose combination produces white light.

Complimentary colour - 'Why, Green, you are looking stunning today!' 'Oh do be quiet, Purple, you're making me blush.'

Complementary medicine - a treatment that is designed to work in conjunction with your body's own resources.

Complimentary medicine - the free samples given out by drug pushers to increase their market.

'My compliments to the chef.' - Please pass on my congtratulations to the person who created this fine meal.

'My complements to the chef.' - Whoever made this meal needs my help.

A compliments slip - small piece of paper to show gratitude to a client for their business.

A complements slip - something you accidentally blurt out that enables your opponent to complete the quiz before you.

Complimenting a woman - noticing she has had her hair done and saying how nice she looks.

Complementing a woman - Well, I've never heard it called that before.

Complementary software - Additional software that completes or enhances an existing offering.

Complimentary software - Thank you for installing AOL.