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About: Complex Numbers

Module by: Don Johnson

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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)
Version: 2.27 (history)
Created: Aug 2, 2000 12:00 am GMT-5
Revised: Aug 9, 2008 6:22 pm GMT-5

Version History

Version: 2.27 Aug 9, 2008 6:22 pm GMT-5 by Don Johnson
Changes: 
Improved the presentation of complex division.
Version: 2.26 Aug 8, 2008 3:01 pm GMT-5 by Don Johnson
Changes: 
Changed the prose concerning j.
Version: 2.25 Aug 2, 2008 11:40 am GMT-5 by Don Johnson
Changes: 
Added a beginning segue.
Version: 2.24 Jul 30, 2008 5:30 pm GMT-5 by Don Johnson
Changes: 
Rearranged groups of equations into tables.
Version: 2.23 Jul 28, 2008 4:02 pm GMT-5 by Don Johnson
Changes: 
Fixed a minor spelling error.
Version: 2.22 Aug 9, 2007 9:39 am GMT-5 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 GMT-5 by Don Johnson
Changes: 
Fixed a minor formatting problem.
Version: 2.20 Apr 12, 2005 4:32 pm GMT-5 by Charlet Reedstrom
Changes: 
update to cnxml-0.5, fix typos, update mathml
Version: 2.19 Aug 26, 2002 12:00 am GMT-5 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 GMT-5 by (Unknown)
Changes: 
Reordered a math display.
Version: 2.17 Aug 13, 2002 12:00 am GMT-5 by (Unknown)
Changes: 
Upgraded to 0.4.
Version: 2.16 Aug 5, 2002 12:00 am GMT-5 by (Unknown)
Changes: 
Fixed minor typos.
Version: 2.15 May 28, 2002 12:00 am GMT-5 by (Unknown)
Changes: 
Added link to the complex plane.
Version: 2.14 Apr 19, 2002 12:00 am GMT-5 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 GMT-5 by Brent Hendricks
Changes: 
Converted to CNXML 0.3.5
Version: 2.12 Aug 27, 2001 12:00 am GMT-5 by (Unknown)
Changes: 
- added missing exercise at the end
Version: 2.11 Aug 24, 2001 12:00 am GMT-5 by (Unknown)
Changes: 
Changed all the subscript errors.
-erin
Version: 2.10 Aug 24, 2001 12:00 am GMT-5 by (Unknown)
Changes: 
i changed an equation so it would be right.
-erin
Version: 2.9 Aug 24, 2001 12:00 am GMT-5 by (Unknown)
Changes: 
Changed keywords.
Version: 2.8 Aug 23, 2001 12:00 am GMT-5 by (Unknown)
Changes: 
no changes
Version: 2.7 Aug 23, 2001 12:00 am GMT-5 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 GMT-5 by (Unknown)
Changes: 
correcting some math errors.
Version: 2.5 Jul 17, 2001 12:00 am GMT-5 by (Unknown)
Changes: 
added keywords
made John Cottrell a maintainer
fixed minor errors
Version: 2.4 Jun 5, 2001 12:00 am GMT-5 by (Unknown)
Changes: 
Fixed emphasis, added an abstract, fixed the display of some equations.
Version: 2.3 Jun 4, 2001 12:00 am GMT-5 by (Unknown)
Changes: 
Upgraded to cnxml version 0.3
Version: 2.2 May 30, 2001 12:00 am GMT-5 by (Unknown)
Changes: 
Just getting rid of the "C"
Version: 2.1 May 29, 2001 12:00 am GMT-5 by (Unknown)
Changes: 
Upgraded to cnxml version 0.3
Version: 2.0 Aug 17, 2000 12:00 am GMT-5 by Brent Hendricks
Changes: 
Bumped version to 2.0

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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, Connexions Web site. http://cnx.org/content/m0081/2.27/, Aug 9, 2008.

American Medical Assocation (AMA) Manual of Style:

Johnson D. Complex Numbers [Connexions 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 Connexions Web site: http://cnx.org/content/m0081/2.27/

Chicago Manual of Style (Bibliography):

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

Chicago Manual of Style (Note):

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

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

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

Modern Languages Association (MLA) Style Manual:

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