Multiplicative Identity
Pronunciation: /ˈmʌl.tɪ.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.
Examples
3 · 1 = 3
^{-}4 · 1 = ^{-}4
p · 1 = p
^{-}t · 1 = ^{-}t
(4 + 2i) · (1 + 0i) = (4 + 2i)
References
- McAdams, David E.. All Math Words Dictionary, multiplicative identity. 2nd Classroom edition 20150108-4799968. pg 121. Life is a Story Problem LLC. January 8, 2015. Buy the book
- Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pg 17. www.archive.org. International Textbook Company. January 1963. Last Accessed 9/2/2018. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n18/mode/1up. Buy the book
- Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pp 29-30. Thomson, Brooks/Cole, 2005.. Last Accessed 9/2/2018. Buy the book
- Mary Jane Sterling. Algebra II For Dummies. pg 12. For Dummies. June 19, 2006. Last Accessed 9/2/2018. Buy the book
More Information
- McAdams, David E.. Identity. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2/11/2010. http://www.allmathwords.org/en/i/identity.html.
Cite this article as:
McAdams, David E. Multiplicative Identity. 4/25/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/m/multiplicativeidentity.html.
Revision History
4/25/2019: Changed equations and expressions to new format. (
McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
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.)