Multiplicative Identity

Pronunciation: /ˈmʌl tə plɪˌkeɪ tɪv aɪˈdɛn tɪ ti/ Explain

An multiplicative identity is the value that, when multiplied by any other values in a set, returns the other value. For real numbers, the multiplicative identity is 1. This is a result of the multiplicative property of 1: for any real number a, a · 1 = a.

For complex numbers the multiplicative identity is 1 + 0i which can also be written 1.


3 · 1 = 3

-4 · 1 = -4

p · 1 = p

-t · 1 = -t

(4 + 2i) · (1 + 0i) = (4 + 2i)


  1. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pg 17. International Textbook Company. January 1963. Last Accessed 1/12/2010. Buy the book
  2. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pp 29-30. Thomson, Brooks/Cole, 2005.. Buy the book
  3. Mary Jane Sterling. Algebra II For Dummies. pg 12. For Dummies. June 19, 2006. Last Accessed 2/11/2010. Buy the book

More Information

  • McAdams, David E.. Identity. All Math Words Encyclopedia. Life is a Story Problem LLC. 2/11/2010.

Cite this article as:

McAdams, David E. Multiplicative Identity. 9/4/2018. All Math Words Encyclopedia. Life is a Story Problem LLC.

Revision History

9/4/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
12/14/2008: Added definition of multiplicative property of 1. (McAdams, David E.)
6/16/2008: Added multiplicative identity for complex numbers. (McAdams, David E.)
6/7/2008: Corrected spelling errors. (McAdams, David E.)
5/29/2008: Fixed grammar error. (McAdams, David E.)
4/17/2008: Initial version. (McAdams, David E.)

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