compliment / complement
One is a nice thing you say. One is a thing that completes another.
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Wrong: The wine complimented the meal.
Right: The wine complemented the meal.
It completed it. E for complete.
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Wrong: She paid me a complement.
Right: She paid me a compliment.
Praise. I for I like it.
The mnemonic
Complement completes. Both have an E in the middle, and one is the definition of the other.
Compliment is the nice one—I like it.
Where it shows up
Complement turns up constantly in design and engineering writing—complementary colours, a complementary skill set, a full complement of staff. All of those mean “completes the set,” and all of them get spelled with an I by people paying a compliment they didn’t intend.
Now go pay someone a real one.