Complement completes or goes with. Compliment praises. The extra i is the praise. The graph complements the table. She complimented the writing. Diction as a set is in word choice.
Complete versus praise
If the sentence is about two parts that fit together, use complement. If someone is saying something nice, use compliment. Complementary angles are a math word from the same root, not a praise word.
Affect versus effect is in affect versus effect. Then versus than is in then versus than. Grammar overall is in ACT grammar rules.
The bottom line
Completes: complement. Praises: compliment.
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