OpenStax CNX

Sections
You are here: Home » Content » Complex Numbers

About: Complex Numbers

Module by: Don Johnson. E-mail the author

View the content: Complex Numbers

Metadata

Name: Complex Numbers
ID: m0081
Language: English (en)
Summary: An introduction to complex numbers.
Subject: Mathematics and Statistics
Keywords: angle of complex number, Cartesian form, complex number, imaginary number, imaginary part, magnitude of complex number, polar form
License: Creative Commons Attribution License CC-BY 3.0

Authors: Don Johnson (dhj@rice.edu)
Copyright Holders: Don Johnson (dhj@rice.edu)
Maintainers: Don Johnson (dhj@rice.edu), Joe Montgomery (montgom@rice.edu), John Cottrell (jac3@rice.edu)

Latest version: 2.29 (history)
First publication date: Aug 2, 2000 12:00 am -0500
Last revision to module: May 15, 2013 7:41 pm -0500

Downloads

PDF: m0081_2.29.pdf PDF file, for viewing content offline and printing. Learn more.
EPUB: m0081_2.29.epub Electronic publication file, for viewing in handheld devices. Learn more.
XML: m0081_2.29.cnxml XML that defines the structure and contents of the module, minus any included media files. Can be reimported in the editing interface. Learn more.
Source Export ZIP: m0081_2.29.zip ZIP containing the module XML plus any included media files. Can be reimported in the editing interface. Learn more.
Offline ZIP: m0081_2.29_offline.zip An offline HTML copy of the content. Also includes XML, included media files, and other support files. Learn more.

Version History

Version: 2.29 May 15, 2013 7:41 pm -0500 by Don Johnson
Changes:
Fixed minor typos.

Version: 2.28 Jan 27, 2013 12:51 pm -0600 by Don Johnson
Changes:
Fixed an error in an expression.

Version: 2.27 Aug 9, 2008 6:22 pm -0500 by Don Johnson
Changes:
Improved the presentation of complex division.

Version: 2.26 Aug 8, 2008 3:01 pm -0500 by Don Johnson
Changes:
Changed the prose concerning j.

Version: 2.25 Aug 2, 2008 11:40 am -0500 by Don Johnson
Changes:
Added a beginning segue.

Version: 2.24 Jul 30, 2008 5:30 pm -0500 by Don Johnson
Changes:
Rearranged groups of equations into tables.

Version: 2.23 Jul 28, 2008 4:02 pm -0500 by Don Johnson
Changes:
Fixed a minor spelling error.

Version: 2.22 Aug 9, 2007 9:39 am -0500 by Don Johnson
Changes:
Rewrote the entire module to improve the presentation and added more problems.

Version: 2.21 Jun 3, 2007 11:17 pm -0500 by Don Johnson
Changes:
Fixed a minor formatting problem.

Version: 2.20 Apr 12, 2005 4:32 pm -0500 by Charlet Reedstrom
Changes:
update to cnxml-0.5, fix typos, update mathml

Version: 2.19 Aug 26, 2002 12:00 am -0500 by (Unknown)
Changes:
Fixed error: hd i^3=-1 and correct to be i^3=-i.

Version: 2.18 Aug 17, 2002 12:00 am -0500 by (Unknown)
Changes:
Reordered a math display.

Version: 2.17 Aug 13, 2002 12:00 am -0500 by (Unknown)
Changes:
Upgraded to 0.4.

Version: 2.16 Aug 5, 2002 12:00 am -0500 by (Unknown)
Changes:
Fixed minor typos.

Version: 2.15 May 28, 2002 12:00 am -0500 by (Unknown)
Changes:
Added link to the complex plane.

Version: 2.14 Apr 19, 2002 12:00 am -0500 by (Unknown)
Changes:
changed a lot of presentation math to content, js to imaginaryi, superscript * to conjugate etc

Version: 2.13 Sep 11, 2001 12:00 am -0500 by Brent Hendricks
Changes:
Converted to CNXML 0.3.5

Version: 2.12 Aug 27, 2001 12:00 am -0500 by (Unknown)
Changes:
- added missing exercise at the end

Version: 2.11 Aug 24, 2001 12:00 am -0500 by (Unknown)
Changes:
Changed all the subscript errors.
-erin

Version: 2.10 Aug 24, 2001 12:00 am -0500 by (Unknown)
Changes:
i changed an equation so it would be right.
-erin

Version: 2.9 Aug 24, 2001 12:00 am -0500 by (Unknown)
Changes:
Changed keywords.

Version: 2.8 Aug 23, 2001 12:00 am -0500 by (Unknown)
Changes:
no changes

Version: 2.7 Aug 23, 2001 12:00 am -0500 by (Unknown)
Changes:
I changed the math for real and imaginary numbers so they are actually recognized as entities.

Version: 2.6 Aug 22, 2001 12:00 am -0500 by (Unknown)
Changes:
correcting some math errors.

Version: 2.5 Jul 17, 2001 12:00 am -0500 by (Unknown)
Changes:
added keywords
made John Cottrell a maintainer
fixed minor errors

Version: 2.4 Jun 5, 2001 12:00 am -0500 by (Unknown)
Changes:
Fixed emphasis, added an abstract, fixed the display of some equations.

Version: 2.3 Jun 4, 2001 12:00 am -0500 by (Unknown)
Changes:
Upgraded to cnxml version 0.3

Version: 2.2 May 30, 2001 12:00 am -0500 by (Unknown)
Changes:
Just getting rid of the "C"

Version: 2.1 May 29, 2001 12:00 am -0500 by (Unknown)
Changes:
Upgraded to cnxml version 0.3

Version: 2.0 Aug 17, 2000 12:00 am -0500 by Brent Hendricks
Changes:
Bumped version to 2.0

How to Reuse and Attribute This Content

If you derive a copy of this content using a OpenStax_CNX account and publish your version, proper attribution of the original work will be automatically done for you.

If you reuse this work elsewhere, in order to comply with the attribution requirements of the license (CC-BY 3.0), you must include

  • the authors' names: Don Johnson
  • the title of the work: Complex Numbers
  • the OpenStax_CNX URL where the work can be found: http://cnx.org/content/m0081/2.29/

See the citation section below for examples you can copy.

How to Cite and Attribute This Content

The following citation styles comply with the attribution requirements for the license (CC-BY 3.0) of this work:

American Chemical Society (ACS) Style Guide:

Johnson, D. Complex Numbers, OpenStax_CNX Web site. http://cnx.org/content/m0081/2.29/, May 15, 2013.

American Medical Assocation (AMA) Manual of Style:

Johnson D. Complex Numbers [OpenStax_CNX Web site]. May 15, 2013. Available at: http://cnx.org/content/m0081/2.29/.

American Psychological Assocation (APA) Publication Manual:

Johnson, D. (2013, May 15). Complex Numbers. Retrieved from the OpenStax_CNX Web site: http://cnx.org/content/m0081/2.29/

Chicago Manual of Style (Bibliography):

Johnson, Don. "Complex Numbers." OpenStax_CNX. May 15, 2013. http://cnx.org/content/m0081/2.29/.

Chicago Manual of Style (Note):

Don Johnson, "Complex Numbers," OpenStax_CNX, May 15, 2013, http://cnx.org/content/m0081/2.29/.

Chicago Manual of Style (Reference, in Author-Date style):

Johnson, D. 2013. Complex Numbers. OpenStax_CNX, May 15, 2013. http://cnx.org/content/m0081/2.29/.

Modern Languages Association (MLA) Style Manual:

Johnson, Don. Complex Numbers. OpenStax_CNX. 15 May 2013 <http://cnx.org/content/m0081/2.29/>.