Complimentary with an i is used when something is free or when you give someone a compliment. Complement with an e means something that completes something else as when two things go well together.
What is difference between complementary and complimentary?
Complimentary (from compliment) means admiring, approving, or flattering—or it can also mean free (like those complimentary chocolates hotels leave on your pillow). Complementary (from complement) means balancing, matching, or completing.
Is there two ways to spell complementary?
When you want to describe something that is "complementary," two or more parts that work together well, think of the word "complete": "Complementary" things complete one another, and both have an "e" in their second syllable.