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About: Complex Numbers

Module by: Don Johnson. E-mail the author

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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
Document Type: -//CNX//DTD CNXML 0.5 plus MathML//EN
License: Creative Commons Attribution License CC-BY 1.0

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: 2.27 (history)
First publication date: Aug 2, 2000 12:00 am -0500
Last revision to module: Aug 9, 2008 6:22 pm -0500

Downloads

PDF: m0081_2.27.pdf PDF file, for viewing content offline and printing. Learn more.
XML: m0081_2.27.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.

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 Currently viewing this version.
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

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  • 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/m0081/2.27/

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How to Cite and Attribute This Content

The following citation styles comply with the attribution requirements for the license (CC-BY 1.0) of this work:

American Chemical Society (ACS) Style Guide:

Johnson, D. Complex Numbers, OpenStax-CNX Web site. http://cnx.org/content/m0081/2.27/, Aug 9, 2008.

American Medical Assocation (AMA) Manual of Style:

Johnson D. Complex Numbers [OpenStax-CNX Web site]. August 9, 2008. Available at: http://cnx.org/content/m0081/2.27/.

American Psychological Assocation (APA) Publication Manual:

Johnson, D. (2008, August 9). Complex Numbers. Retrieved from the OpenStax-CNX Web site: http://cnx.org/content/m0081/2.27/

Chicago Manual of Style (Bibliography):

Johnson, Don. "Complex Numbers." OpenStax-CNX. August 9, 2008. http://cnx.org/content/m0081/2.27/.

Chicago Manual of Style (Note):

Don Johnson, "Complex Numbers," OpenStax-CNX, August 9, 2008, http://cnx.org/content/m0081/2.27/.

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

Johnson, D. 2008. Complex Numbers. OpenStax-CNX, August 9, 2008. http://cnx.org/content/m0081/2.27/.

Modern Languages Association (MLA) Style Manual:

Johnson, Don. Complex Numbers. OpenStax-CNX. 9 Aug. 2008 <http://cnx.org/content/m0081/2.27/>.