complement
A complement is something that makes up a satisfying whole with something else. Those shiny red shoes you just bought complement your shiny red purse.
compliment
A compliment is an expression of respect or admiration, like, "You're such a good writer," or "You know so many words!" Keep them coming.
I was taking notes during a meeting this morning and typed the word "complementary" on the screen. One of my coworkers said the same thing. She never knew it was spelled that way. And thus, a post was born on Phuks and Poal.
I always admire people who can learn English well. We have so many confusing spellings and words like the different ways to spell pore/pour/poor for example, but all said the same way. It really is a mongrel language.
I actually had no idea there was a difference in spelling. Huh, TIL.