complementary, complimentary

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.

complementary
  1. :: adjective

    Biochemistry Of or relating to the specific pairing of the purines and pyrimidines between strands of a DNA or an RNA molecule.

  2. :: adjective

    Genetics Of or relating to a group of genes that act in concert to produce a specific phenotype.

  3. :: adjective

    Supplying mutual needs or offsetting mutual lacks.

  4. :: adjective

    Forming or serving as a complement; completing.

complimentary
  1. :: adjective

    Given free to repay a favor or as an act of courtesy: complimentary copies of the new book.

  2. :: adjective

    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.

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About Homophones

Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.

If they are spelled the same then they are also homographs (and homonyms); if they are spelled differently then they are also heterographs (literally "different writing").