You might think the quality of a proofreader is determined by how well they catch typos. I propose that the quality of a proofreader is determined by how much agony he or she feels when they miss one.
True story: When I was just a wee proofreader first starting out, a client pulled me aside and pointed out that there were, in fact, two ways to spell complimentary/complementary. I cried for days (okay, that last part is not exactly true). But I DID agonize for days over it. DON’T LET THIS HAPPEN TO YOU!
Think of it this way:
There is COMPLIMENTARY with an I and COMPLEMENTARY with an E.
COMPLIMENTS are free. Anything that is free is COMPLIMENTARY.
Things that go well together are COMPLEMENTARY. The two Es in COMPLEMENTARY go well together.