Additive Identity

Pronunciation: /ˈæd ɪ tɪv aɪˈdɛn tɪ ti/ Explain

The additive identity of a number is the value that, when added to the number, returns that number.[1] For real numbers, the additive identity is 0. This is because for any real number a, a + 0 = a.

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


3 + 0 = 3
-4 + 0 = -4
p + 0 = p
-t + 0 = -t
(4 + 2i) + (0 + 0i) = (4 + 2i)


  1. additive identity. Encyclopedia Britannica. Merriam-Webster. Last Accessed 8/6/2018. identity.
  2. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pg 17. International Textbook Company. January 1963. Last Accessed 8/6/2018. Buy the book
  3. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pp 29-30. Thomson, Brooks/Cole. 2005. Buy the book
  4. Mary Jane Sterling. Algebra II For Dummies. pg 12. For Dummies. June 19, 2006. Last Accessed 8/6/2018. Buy the book

More Information

  • McAdams, David E.. Identity. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/19/2018.

Cite this article as:

McAdams, David E. Additive Identity. 6/12/2018. All Math Words Encyclopedia. Life is a Story Problem LLC.

Revision History

6/18/2018: Clarified wording. (McAdams, David E.)
6/12/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
12/24/2009: Added "References". (McAdams, David E.)
2/18/2009: Corrected math error. (McAdams, David E.)
10/5/2008: Expanded 'More Information'. (McAdams, David E.)
6/16/2008: Added additive 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.)

All Math Words Encyclopedia is a service of Life is a Story Problem LLC.
Copyright © 2018 Life is a Story Problem LLC. All rights reserved.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License