# Euler's Formula

Pronunciation: /ˈɔɪ.lərz ˈfɔɹ.mjə.lə/ Explain

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Euler's formula is .[2] It is remarkable in that it relates trigonometric function functions with complex numbers. Euler's formula maps the natural constant e raised to the complex exponent to the complex plane using the trigonometric expression . This equation is true only if the angle θ is measured in radians.

Euler's formula is named after Leonhard Euler who published it in its present form in 1748.

Leonard Euler was a very prolific mathematician. Note that the phrase Euler's Formula is used to indicate different formulas in different disciplines.

### References

1. McAdams, David E.. All Math Words Dictionary, euler's formula. 2nd Classroom edition 20150108-4799968. pg 73. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Paul J. Nahin. Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills. Princeton University Press. April 10, 2006. Last Accessed 7/9/2018. Buy the book
3. Fine, Henry B., Ph. D.. Number-System of Algebra Treated Theoretically and Historically. 2nd edition. pg 30. www.archive.org. D. C. Heath & Co., Boston, U.S.A.. 1907. Last Accessed 7/9/2018. http://www.archive.org/stream/thenumbersystemo17920gut/17920-pdf#page/n39/mode/1up. Buy the book

McAdams, David E. Euler's Formula. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/e/eulersformula.html.

### Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)