A compliment is when someone says something nice. The review was a compliment because it said nice things, and gave the book four stars. Compliment is spelled with an I that looks like a person who is saying something.
A complement is something that makes another thing complete. A complementary color is on the opposite side of the color wheel. When both colors are mixed, all three primary colors are present. It's spelled with an e that looks like a color wheel that is divided in half.
The review was a complement because the reviewer sent me a private email that included a list of typos I didn't catch. One of them was the word complement, which sent me running to the dictionary to see what he meant. One of them was a glaring mistake. So, if you're planning on buying the book, please give me a week to correct those mistakes. I want you to have the best book I can write.