Talk:Complex number
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Exercise Needed
everything fine there in the article. as an encyclopeadian article. but shouldn't there be exercises? --jai 12:20, Aug 13, 2004 (UTC)
{{msg:quantity}}
I don't see that {{msg:quantity}} hurt this page in any way. It seems like a generally good idea. Why remove it? -rs2 00:27, 29 Mar 2004 (UTC)
Removed text
In the discussion of the argument of a complex number, I removed the following:
- Note that this is exactly the same problem encountered when trying to define the inverse tangent as a function. The connection becomes more transparent when one considers that the formula for calculating arg(z) is arg(z) = arctan(b/a) if z = a + i b.
The values of the arctan function lie between -Pi/2 and +Pi/2, while arguments of complex numbers lie between -Pi and +Pi. The arctan formula for arg(z) is therefore incorrect. Most programming language have a function atan2(b, a) which returns the proper argument of a + i b by taking the signs of a and b into account. --AxelBoldt
Spanish translation
You can see the translation to spanish in --Atlante
Graphical explanation
A graphical explanation is better than words. Should add images sometime. --Wshun
De Moivre's formula
I could not find Demovire's theorem for complex numbers,should add this.-Raj.B (India-Karnataka-Mysore)
- It's at De Moivre's formula. I've put a link to it in the article. --Zundark 10:18, 13 Dec 2003 (UTC)
Was this copied?
Is this page originally copied from somewhere? -- Walt Pohl 18:04, 13 Mar 2004 (UTC)
- Looks like it to me. Sounds rather archaic (1890-ish, perhaps). Probably public domain, but would be good to know where it comes from. Gwimpey 23:21, May 24, 2005 (UTC)
Proper fields isomorophic
Can someone give an example of a proper subfield of C isomorphic to C, or at least show one exists? I'm not saying I think it's not true; I just don't remember seeing this, so I'm interested how it's done. Revolver 13:49, 2 Nov 2004 (UTC)
- There's an argument showing that these subfields exist at the end of the transcendence degree article. -- Fropuff 16:22, 2004 Nov 2 (UTC)
- I get it. I think a comment saying that it's not constructive, that the axiom of choice is used, and so no such explicit subfield can be produced, would be good to say. Revolver 19:46, 2 Nov 2004 (UTC)
j or i - usage of the imag. unit in maths, physics, electrotechnology
According to the person sitting next to me, the root of negative one is represented by j not i now. Someone had better change it all.
Engineers tend to use <math>j<math>, and mathematicians <math>i<math>.
Robinh 13:52, 24 May 2005 (UTC)
Yes, as far as I could observe, mathematicians and physicists prefer using i as the imaginary unit, while electrical engineering technicians prefer j as the character for the imaginary unit. For me (physicist) it does not matter, whether i or j is used in formulas. If they are written in non-italic characters, then a clear seperation from alternating current i and counting indexes like i or j is very easy. Originally, in electrical engineering the j was used to prevent confusion of imaginary unit i with the alternating current i. But I have not observed problems with this similarity, if italic and non-italic characters are used correctly. Nevertheless, on manually written pages, in any case a small legend of the used characters should be listed anyway, and there the non-italic symbol for the imaginary unit (i or j) can be clearly assigned. Personally, I prefer i as the imaginary unit, but because i = j = 'imaginary unit' both can be mixed/exchanged without problems.
Enjoy working with the imaginary unit ! Wurzel 10:00 UTC, 29 May 2005
The non-italic writing style of the imaginary unit
causes the lowest amount of trouble, if the imaginary unit i (mostly used in mathematics, physics), or j - frequently used in electrical engineering is written in non-italic writing style. I have observed this in the recent decade of my work in science, and a clear seperation of italic charactes for variables e.g. a,b, and non-italic characters for 'units' for which we also can count the 'imaginary unit' seems to be the best solution. This prevents mixing up the 'imaginary unit' i with e.g. the current i.
Books with a high scientific level and a high acceptance prefer using this way. To them belong (upper part of the table):
| References | imag. unit | comment |
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| Haken, Wolf; Molecule- and Quantum Physics, 1.-8. ed. | i | |
| Haken, Wolf; Atomics- and Quantum Chemistry, 1.-8. ed. | i | |
| Slichter; Principles of Magnetic Resonance 1.-3. ed. | i | |
| A.C.S. van Heel; Advanced Optical Techniques, 1967, Delft, Holland, 1st ed. | i | |
| Nightingale; A short course in General Relativity, 1986, 2nd ed. | i | |
| References (with tendencially problemat. notation) | imag. unit | Comment |
| www.wikipedia.fr : 'Nombre complexe', on 9.3.2005 14:45 CET | <math>\vec{i}<math> | Hmm, is also an interesting alternative |
| Griffiths-Harris: Principles of Algebraic Geometry | <math>\sqrt{-1}<math> | makes the formulas quite cumbersome |
| N. Minorsky; Nonlinear Oscillators, 1962, New Jersey, 1st ed. | i | i is also used for indexes and as alternating current i see p.174 |
| L.B. Felsen, N. Marcuvitz; Radiation and Scattering of Waves, 1973, 1st ed. | i,j | both are used dependent on chapter |
[I will update this list, as soon as I have newer data.]
If somebody has other/better proposals then he can offer them.
- I have a solution: change it back to italics. You are proposing a radical change in notation. Virtually all math textbooks use italicized i for imaginary unit. There are other variables to use for an index besides i. Like n. Or k. If you need i for current, use j then. But don't pretend non-italicized i is such that
"Books with a high scientific level and a high acceptance prefer using this way."
Give me a break. Are you saying that all the graduate and research math textbooks and papers I have aren't of a high scientific level or high acceptance?? I noticed all your "high level books" are of a particular area or field, namely physics. Physicists aren't the only people to use i. BTW, I think the algebraic geometry Griffiths-Harris example may not be appropriate, as in abstract algebra one often uses sqrt(-1) as opposed to i, because one is working in fields other than the complex numbers, where square roots of -1 exist, but are not "the imaginary unit" because we're not in the complex field. Revolver 09:04, 8 Jun 2005 (UTC)