Talk:Complex plane

message: I believe the following passage is incorrect: "The unit circle itself (|z| = 1) will be mapped onto the equator, and the exterior of the unit circle (|z| > 1) will be mapped onto the northern hemisphere,..."
Actually, I believe the equator is mapped onto |z| = 2.  — Preceding unsigned comment added by 178.190.43.45 (talk) 20:20, 27 December 2012 (UTC)
thread_title:  Comment by Karl 

message: Whoops, confused Bode plots with Nyquist plots there for a moment. Fixed now. -- The Anome 22:17, 2 October 2005 (UTC)
replies: text: Wouldn't that just be a complex function of a real variable? They certainly have been considered and studied. Madmath789 18:24, 9 September 2006 (UTC)

text: I've actually thought about that idea before as well, though I don't know enough about mathematics to form any sort of conclusion on that yet. --Neko18 00:34, 11 November 2006 (UTC)
thread_title:  Comment by User:The Anome 

message: I've been adding quite a bit of new content to this article recently, in response to the "stub" tags. My general plan to complete the article looks like this.
# Explain the connection between the Cartesian plane and the (traditional) complex plane. (done)
# Explain the representation of the extended complex plane as a sphere. (done)
# Explain various motivations for "cutting" the plane. (done)
# Explain the process of "gluing" cut planes (sheets) together to form Riemann surfaces. (pending)
# Allude to alternative "complex planes", specifically C×C. (pending)
Can you think of anything important that I've left out? I've put in quite a few examples, because I think people who are curious but not really mathematicians might read this article. Are there too many examples? My aim was to introduce infinite products, infinite sums, and continued fractions within this one article, just to pique the reader's curiosity. Is that a good strategy? Or not?
Your feedback is welcome, either on this talk page or on my user talk page.  DavidCBryant 16:02, 4 January 2007 (UTC)
replies: text: In response to your note on my talk page, and to the above, I do appreciate the new content. As for the relative prominence of the various planes, one might note from Euclidean geometry#Treatment using analytic geometry that the ordinary complex plane has great utility in geometry. Such utility for the other planes exists but needs communcation to the wider community of users of quatitative methods. The lack of departmental boundaries in WP gives me hope, for instance, that the split-complex number plane will become well enough known that the obscurantism practiced in the name of spacetime physical science can be overcome.Rgdboer 21:49, 10 January 2007 (UTC)

text: The first two sentences in the article are excellent for motivating the alternative complex planes: the paragraph could be extended to say "If i represents the imaginary unit, then i2 ∈ {−1, 0, +1}. This article treats the case ii = −1 ; see dual numbers for ii = 0 and split-complex numbers for ii = +1."Rgdboer 04:59, 12 January 2007 (UTC)
thread_title:  New content 

message: Where does real Coffee fit in an Argand plane? —The preceding unsigned comment was added by 82.211.73.34 (talk) 12:23, 1 February 2007 (UTC)
thread_title:  Real Coffee  

message: Argand diagram redirects here, but Argand Diagram redirects to Complex Number. Surely they should both go to the same place?--Physics is all gnomes (talk) 14:14, 31 December 2010 (UTC)
thread_title: Weird redirects

message: The issue of other complex planes arose when Hartenberg and Denavit were preparing appendix A-1 (pp 370–9) of Kinematic Synthesis of Linkages. In the footnote on page 372 one reads
:Rather, c = a + b i  should be called the ordinary, or usual, complex number. There are others, for example c = a + ω b, where it is agreed that ω2 = 0. These are not our concern at this time.
The most immediate context in which the triple of canonical complex planes is necessary for comprehension is in the algebra of 2 × 2 real matrices. This reference has been posted here to backstop the footnote to the lead.Rgdboer (talk) 02:59, 14 April 2011 (UTC)
thread_title:  Other complex planes 

message: This article mentions Argand diagrams (and indeed, it is the redirect for it) but it doesn't explain what they are or provide a labeled example.  I can see how that might appear trivial but there should at least be a full definition or sample construction. 76.181.233.121 (talk) 18:37, 17 June 2016 (UTC)
thread_title:  Argand diagrams