Multiplicative Identity

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

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.

Examples

3 · 1 = 3

-4 · 1 = -4

p · 1 = p

-t · 1 = -t

(4 + 2i) · (1 + 0i) = (4 + 2i)

References

  1. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry, pg 17. International Textbook Company, January 1963. (Accessed: 2010-01-12). http://www.archive.org/stream/algebraandtrigon033520mbp#page/n18/mode/1up.
  2. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra, 6th edition, pp 29-30. Thomson, Brooks/Cole, 2005.
  3. Mary Jane Sterling. Algebra II For Dummies, pg 12. For Dummies, June 19, 2006. (Accessed: 2010-02-11).

More Information

  • McAdams, David. Identity. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2010-02-11. http://www.allmathwords.org/article.aspx?lang=en&id=Identity.

Printed Resources

Cite this article as:


Multiplicative Identity. 2008-12-14. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/m/multiplicativeidentity.html.

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Revision History


2008-12-14: Added definition of multiplicative property of 1 (McAdams, David.)
2008-06-16: Added multiplicative identity for complex numbers (McAdams, David.)
2008-06-07: Corrected spelling errors (McAdams, David.)
2008-05-29: Fixed grammar error (McAdams, David.)
2008-04-17: Initial version (McAdams, David.)

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