# 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

1. 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
2. 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
3. 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
4. Mary Jane Sterling. Algebra II For Dummies. pg 12. For Dummies. June 19, 2006. Last Accessed 9/2/2018. Buy the book

• McAdams, David E.. Identity. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2/11/2010. https://www.allmathwords.org/en/i/identity.html.

McAdams, David E. Multiplicative Identity. 4/25/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://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.)