Talk:Imaginary unit

Merge into Imaginary number?

Isheden said above:

Rather than changing the title to something with "imaginary number", why not merge this article into imaginary number? The articles have a large overlap, which merits merging, see WP:Merging. Isheden (talk) 16:41, 8 January 2012 (UTC)

• Support. There is already a merge proposal on these two pages, and imaginary number is a far more widely familiar term than imaginary unit. And Imaginary number doesn't contain any parentheses. Duoduoduo (talk) 18:42, 8 January 2012 (UTC)

• Oppose. As partially explained elsewhere, in my opinion "imaginary unit" is worthy of its own article. Additionally I don't see that this question really has much to do with the above discussion. Paul August ☎ 19:12, 8 January 2012 (UTC)

  Well, it's not in the above section. Nevertheless, it's relevance to the above discussion is that if we merge this article into Imaginary number, the above discussion of the best name for this article becomes moot. Duoduoduo (talk) 8 January 2012

• Support I don't find any of the arguments against a merge between the two articles convincing. Isheden (talk) 20:07, 8 January 2012 (UTC)

• Support I disagree that the imaginary unit is worthy of its own article; it makes most sense in the context of complex numbers. In that article it deserves a section. But if it is only merged into Imaginary number, this would also be better than the current article. — Quondum^☏✎ 20:42, 8 January 2012 (UTC)

• Oppose. Shall we merge 1 (number) into Integer too? This is a distinct topic: a specific, notable, and important imaginary number. To a general audience it's certainly notable on its own. Furthermore, avoiding consensus on a title discussion is not a good reason to merge. – Pnm (talk) 22:37, 8 January 2012 (UTC)

• Oppose Pure imaginary numbers are of zero interest outside of some school textbooks. They don't form a field. I can see a section about imaginary numbers under imaginary unit but putting imaginary unit under imaginary number is just wrong. The imaginary unit is something of interest. Imaginary numbes are just marginally more interesting than the multiples of 1+2i. Dmcq (talk) 23:13, 8 January 2012 (UTC)

  Good points. For that reason, a separate article on imaginary numbers is hardly motivated. The question then is what name would be suitable for an article cthat covers pure imaginary numbers in addition to the unit imaginary number. Isheden (talk) 07:51, 9 January 2012 (UTC)

  I concur that imaginary number does not merit an article on its own, and hence this discussion is really about whether i merits its own article, and if so, under what name. One may argue that 2 (number) and the like have their own articles, but they are not, in my opinion, encyclopedic, really being a collection of arbitrary "Did you know...?" facts. To my mind, i falls into this category (as a reading of the article will confirm). It only has true relevance in the specific context of complex numbers. It is not even an identity element. It is exactly equivalent to its twin. It is equivalent to any square root of –1 in a subspace of ℍ isomorphic to ℂ. In short, i is unremarkable unless you know only the algebras ℝ and ℂ. But more to the point: if it is to remain a separate article, it will have value not to mathematicians, but to those with a budding interest in mathematics. And for this audience, "imaginary unit" is obscure, and I guess hardly occurs in literature aimed at this audience. This does not really matter, since redirects take care of this. — Quondum^☏✎ 11:30, 9 January 2012 (UTC)

I think you'll find (if you examine the Google Books search I gave above) that "imaginary unit" occurs frequently in high school texts/first year college texts, dealing with this subject matter. And certainly "Imaginary number is worthy of an article. Paul August ☎ 14:45, 9 January 2012 (UTC)

I was perhaps overhasty about classifying the target audience of the books containing "imaginary unit"; the books with "square root of minus one" are visibly directed at lay people, by contrast presumably people not studying complex analysis at all. If introduced in high school texts, this corresponds to the first formal introduction to the concept, and this weakens my case considerably with regard to target audience. Whether it merits an article on its own is another matter; this is more subjective. About half of the current content of the article strikes me as either belonging in Complex number or being somewhat ad hoc (what is mentionable about i!?). Trimming the article to focus on its defining relation, its relation to its twin −i, its fundamental role in the field of complex numbers, and possibly its analogues in other algebras would make more sense to me. — Quondum^☏✎ 15:39, 9 January 2012 (UTC)

Yes, the formula for i! is a bit arcane but in my view worth being given somewhere, and this seems the logical place. I think it would be very useful to consider the content of the present article in detail, but probably best to do that in another section? Paul August ☎ 18:56, 9 January 2012 (UTC)

I'd also like a bit of history, who first used i for i, Rafael Bombelli's rules for multiplication, that it has been remarked on as a fundamental mathematical constant in Euler's identity. There could be a bit of expansion on how it is just one of the square roots of −1. WIth the stuff about imaginary numbers there quite a bit that is notable but one wouldn't really want in the complex number article. Dmcq (talk) 17:11, 9 January 2012 (UTC)

Agree and Nahin's An Imaginary Tale: The Story of √−1 would be an obvious place to start researching the history question at least, but see my comment above about discussing content issues in another section. Paul August ☎ 18:56, 9 January 2012 (UTC)

For the history of imaginary numbers, start with Tartaglia and Cardano's attempts to solve the cubic equation. Eli Maor's books e: The story of a Number and Trigonometric Delights make for good references for this, too. — Loadmaster (talk) 19:18, 11 January 2012 (UTC)

The book Stalking the Riemann Hypothesis[1] by Dan Rockmore mentions (p.73) that Euler was the first to symbolize the imaginary unit as i. — Loadmaster (talk) 04:14, 28 January 2012 (UTC)

• Oppose. As mentioned by others above, the imaginary unit i is worthy of its own article. — Loadmaster (talk) 19:18, 11 January 2012 (UTC)
• Oppose, Wikipedia has millions of articles, it's got room for three separate ones on the three well-known mathematical concepts of i, imaginary numbers and complex numbers Anyone looking any of them up ought to find it defined and explained immediately (with clearly visible links to other relevant articles, of course). I would hope to see the advanced mathematical information drift towards complex number, leaving the other two as very straightforward articles fully accessible to the mathematically unsophisticated.--Kotniski (talk) 19:49, 11 January 2012 (UTC)
• oppose - they are separate concepts although closely related, both notable enough for their own article, and readers might want to read about one or the other. Generally it's often useful to have articles on related mathematics (and pretty much only mathematics) topics if they look at the common area from different directions, at different speeds or in different amounts of detail. I think that certainly applies here.--JohnBlackburne^words_deeds 00:03, 13 January 2012 (UTC)

Attempt to reach consensus

My impression of the intense discussion above is that we have two groups of people representing different views:

• The first group consists of people who claim that imaginary unit is obscure to the general audience. Therefore, this group would like the constant to have an article name based on the symbol i. However, the best title they have come up with is i (imaginary number), which arguably will not be any easier to find for ordinary people who are not aware of the conventions for disambiguation on Wikipedia. On the other hand, the article imaginary number is considered to have a well-known name and this group is opposed to merging the two articles.

• The second group is perhaps somewhat more mathematically trained and has no problem with the name imaginary unit, because it is the name they are used to for this constant. Instead, they have a problem with changing an unambiguous title to i (something), because the imaginary unit is also commonly denoted by j. These people consider the article imaginary number superfluous and would prefer to merge the two articles.

Moreover, it is interesting to note that Imaginary number is #265 on the List of frequently viewed articles whereas Imaginary unit is not among the 500 most viewed articles in mathematics. It therefore seems that people find their way to imaginary number rather than imaginary unit.

My proposal is as follows. Let's keep the article Imaginary number and aim it specifically at a general audience without assuming them to have any particular mathematical background. It's ok in that article to refer to the square root of -1 and just call it i. However, it should be mentioned that mathematicians call this constant imaginary unit (with a link). On the other hand, let's keep the name Imaginary unit for this article and direct it towards an audience with a little bit more background in mathematics. In this article it might be more appropriate to define the imaginary unit in terms of its property i² = 1. Isheden (talk) 21:43, 12 January 2012 (UTC)

The problem I have with that is that when people look up imaginary number they probably either mean either the imaginary unit or complex numbers and not what the imaginary number article is about. On the other hand some people would be looking it up for exactly what it is about since they have read those textbooks using the name. I think the best solution is to simply have imaginary number be a redirect to an section within imaginary unit which deals specifically with imaginary numbers as reals multiplied by i and then the main article is about i which is probably what most of them wanted. and it refers out to complex number nicely. Redirects can deal with searches well so the name of the article should be the most appropriate one. I like imaginary unit because then I don't have to always pipe the name when referring to the article from elsewhere. Dmcq (talk) 23:30, 12 January 2012 (UTC)

There is a merge proposal immediately above, which would result in the two articles being combined, but it seems unlikely to be agreed and implemented.--JohnBlackburne^words_deeds 23:52, 12 January 2012 (UTC)

That was to merge this article into imaginary number. There is another discussion at Talk:Imaginary number#Proposed merge into imaginary unit which is what the merge tag at the top of the article points at but hardly anyone has contributed to. That one is to merge imaginary number into imaginary unit which I believe could be done easily and would be an improvement as I described just above. Dmcq (talk) 08:19, 13 January 2012 (UTC)

Whatever direction it happens in, my feeling is that having the three separate articles is unnecessary and a little confusing to a newbie reading up on this. IMO, good first step would be to merge imaginary number with the others. Beyond that I imagine we'll be becalmed on the sea of non-consensus. — Quondum^☏✎ 08:51, 13 January 2012 (UTC)

I would say it would be more confusing to newbies if they were merged. If you've heard about imaginary numbers and want to look them up on Wikipedia, the best thing that can happen is that you arrive at a page titled "Imaginary number", which defines and explains them clearly, and contains clear links to articles on the other closely related concepts, that they can then look up to find whatever further information interests them.--Kotniski (talk) 09:02, 13 January 2012 (UTC)

Defines and explains what though is the problem. Yes that article is about imaginary numbers as used in some student textbooks. But imaginary number can also mean the imaginary unit and it can also mean a complex number. Having such a common name be used for describing such a useless concept strikes me as wrong. Dmcq (talk) 12:09, 13 January 2012 (UTC)

Well, if the term has significant usage under different meanings, we certainly need to mention that prominently. But it's not up to us to try to change existing mathematical terminology - and we all know what Re(z) and Im(z) mean (if it was up to me I'd never have called Im(z) the imaginary part of z, either, but that's something else we can do nothing about here).--Kotniski (talk) 12:58, 13 January 2012 (UTC)

I think we need to drop the requirement that the article Imaginary number should define the term clearly, since imaginary number can mean different things partly for historical reasons. A general audience might find a historical exposition with links to the unambiguous terms used in modern mathematics more helpful. The alternative would be a disambiguation page, but this approach would not clarify why the term imaginary number sometimes refers to what is now known as complex numbers, sometimes refers to pure imaginary numbers, sometimes excludes zero, etc. A redirect to a section in this article is logical to a mathematically trained person, but it is not necessarily the way to present the topic to a lay person. Isheden (talk) 13:01, 13 January 2012 (UTC)

i ^i wrong?

WolframAlpha makes it 0.207879576350761908546955619834978.. instead of article's 0.207879576350761908546955465465465.. Who's right? --81.216.218.158 (talk) 00:25, 29 January 2012 (UTC)

Look at that repeat at the end of the figure in the article and think what's the probability of that being true? Dmcq (talk) 00:35, 29 January 2012 (UTC)

Well spotted by the IP. I've trimmed purposeless extra digits, in the process removing the error. — Quondum^☏✎ 15:39, 29 January 2012 (UTC)

Origin of term "imaginary"

The last sentence of the first paragraph reads 'The term "imaginary" is used because there is no real number having a negative square.' I think that is wrong; Gauss coined the term "real" after "imaginary" had been coined and in contradistinction to it. Maybe. Others will know better than I. 81.131.23.34 (talk) 16:08, 27 July 2012 (UTC)

Constant not variable

In this encyclopedia all variables are italicized. But numerals and the constant e are not rendered in the italic font. Why is the imaginary unit written with italics ? Rgdboer (talk) 19:49, 25 September 2012 (UTC)

This has been discussed several times in the past. See e.g. Talk:Complex number/Archive 1#The non-italic writing style of the imaginary unit. And Wikipedia:Manual of Style (mathematics)#Choice of type style currently says

“Special care is needed with subscripted labels to distinguish the purpose of the subscript (as this is a common error): variables and constants in subscripts should be italic, while textual labels should be in normal text font (Roman, upright). … On the other hand, for the differential, imaginary unit, and Euler's number, Wikipedia articles usually use an italic font … Some authors prefer to use an upright (Roman) font for dx, and Roman boldface for i. Both forms are correct; what is most important is consistency within an article. It is considered inappropriate for an editor to go through articles doing mass changes from one style to another. This is much the same principle as the guidelines in the Manual of Style for the colour/color spelling choice, etc.”

So it basically comes down to convention. — Tobias Bergemann (talk) 07:23, 26 September 2012 (UTC)

Thank you for the clarification on convention, consistency, and practice.Rgdboer (talk) 20:58, 26 September 2012 (UTC)