The words complementing, complimenting sound the same but have different meanings and spellings. Why do complementing, complimenting sound the same even though they are completely different words?
The answer is simple: complementing, complimenting are homophones of the English language.
Present participle of complement.
Present participle of compliment.
Definitions from Wiktionary, Creative Commons Attribution/Share-Alike License and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.