The words complementary, complimentary sound the same but have different meanings and spellings. Why do complementary, complimentary sound the same even though they are completely different words?
The answer is simple: complementary, complimentary are homophones of the English language.
Biochemistry Of or relating to the specific pairing of the purines and pyrimidines between strands of a DNA or an RNA molecule.
Genetics Of or relating to a group of genes that act in concert to produce a specific phenotype.
Supplying mutual needs or offsetting mutual lacks.
Forming or serving as a complement; completing.
Given free to repay a favor or as an act of courtesy: complimentary copies of the new book.
Expressing, using, or resembling a compliment: a concert that received complimentary reviews.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.