View source for Talk:Imaginary number

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== first sentence ==

"An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i"  The page [[Complex number]] says "A complex number is a number that can be expressed in the form a + bi".  So does our article mean that an imaginary number is a complex number where a=0?  Or is the definition at Complex number wrong in insisting on 'a'?--[[User:Richardson mcphillips|Richardson mcphillips]] ([[User talk:Richardson mcphillips|talk]]) 14:03, 27 May 2019 (UTC)

also, Complex number says  "...i is a solution of the equation x2 = −1. Because no real number satisfies this equation, i is called an imaginary number."  This is different from the current article.  --[[User:Richardson mcphillips|Richardson mcphillips]] ([[User talk:Richardson mcphillips|talk]]) 14:05, 27 May 2019 (UTC)

:All imaginary numbers are also complex numbers. Yes, our article means that an imaginary number is a complex number where ''a''=0. The definition in [[Complex number]] says: "... where ''a'' and ''b'' are real numbers", so it allows the case ''a''=0.
:And indeed "i is called an imaginary number", as, in this case, the real number multiplied by the imaginary unit i, is 1, which is a real number. So everything is just fine. - [[User:DVdm|DVdm]] ([[User talk:DVdm|talk]]) 14:12, 27 May 2019 (UTC)

== Hero/Heron of Alexandria ==

A recent edit by {{u|PaulHue}} was reverted by {{u|Beauty School Dropout}}. The disagreement is over whether a well known ancient mathematician is called "Hero" or "Heron". I have come disputes over this before, so I thought it might help to clarify the situation. The man's name was Ἥρων, which transliterated into the Latin alphabet is "Heron". However, as with many other ancient Greek names, it is a long established custom in English to used the form of the name which the ancient Romans used, which is not always a literal transliteration of the Greek. In this case the Latin form of the name was "Hero", and that is the form of the name which has been usual in English for many centuries. An exactly parallel name is Πλάτων, which transliterates as "Platon", but the person in question is universally known in English as "[[Plato]]". In recent times some authors have used the form "Heron", and that is the form of the name that I encountered when I was young, and therefore the name under which I normally think of the mathematician in question.

When I started writing this, my intention was merely to explain why there are two different forms of the name in use, for the purpose of clarifying the issue when two or more editors disagree, and stop there. However, it then occurred to me that it might be interesting to see which form of the name is more commonly used in English: is it still "Hero", or has "Heron" now taken over? I found that a Google search for ''-Hero "Heron of Alexandria"'' produced about 71,000 hits, and ''-Heron "Hero of Alexandria"'' 235,000. I am, of course, aware that for various reasons a Google search is not a totally reliable measure of frequency of use, but in this case the result gives so very substantial majority to "Hero", the traditional form in English, that unless and until someone produces more reliable evidence that "Heron" is now the more common, we should prefer "Hero". In addition, the Wikipedia article about him uses "Hero", and there is an advantage in consistency. My own natural preference is for "Heron", since, as I explained above, that is the form which comes more naturally to me, but in light of what I have just said I shall restore the form "Hero" in the article. [[User:JBW|JBW]] ([[User talk:JBW|talk]]) <small>''Formerly known as JamesBWatson''</small> 19:34, 2 October 2019 (UTC)

== Suggesting a section titled: Use of Imaginary Numbers ==

Would this article be improved if a section were added titled, Use of Imaginary Numbers, that mentioned their use in quantum mechanics, electric circuits, calculus,  quadratic planes, and the like? [[User:BobEnyart|Bob Enyart, Denver KGOV radio host ]] ([[User talk:BobEnyart|talk]]) 12:55, 10 April 2020 (UTC)

== Run-on and confusing sentence ==

The following sentence is a run-on sentence and is confusing.

: {{color|#045|An imaginary number bi can be added to a real number a to form a complex number of the form a + bi, where the real numbers a and b are called, respectively, the real part and the imaginary part of the complex number.}}

Would the sentence be clearer (albeit still run-on) if the phrase "i is" were added, as shown below?

: {{color|#045|An imaginary number bi can be added to a real number a to form a complex number of the form a + bi, where the real numbers a and b are called, respectively, the real part and i is the imaginary part of the complex number.}}

<!-- Template:Unsigned --><span class="autosigned" style="font-size:85%;">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:69.137.146.91|69.137.146.91]] ([[User talk:69.137.146.91#top|talk]] • [[Special:Contributions/69.137.146.91|contribs]]) 07:19, 7 April 2021 (UTC)</span>

:<small>Please [[wp:signature|sign]] all your talk page messages with four tildes (<nowiki>~~~~</nowiki>) — See [[Help:Using talk pages]]. Thanks.</small>
: {{not done}}. In the literature, the real number ''a'' is called the ''real part'' and the real number ''b'', being the coefficient of ''i'', is called the ''imaginary part''. Google is your friend. - [[User:DVdm|DVdm]] ([[User talk:DVdm|talk]]) 09:29, 7 April 2021 (UTC)

Now I understand! Thanks so much. Math is good.[[Special:Contributions/69.137.146.91|69.137.146.91]] ([[User talk:69.137.146.91|talk]]) 16:06, 9 April 2021 (UTC)

== Same Articles ==

What is the difference between imaginary number and imaginary unit? of Wikipedia The name of another article is imaginary unit. Aren't these two articles about the same thing? The most logical thing to do is to merge the articles (or delete one of them). [[User:Bera678|Bera678]] ([[User talk:Bera678|talk]]) 16:56, 17 December 2023 (UTC)

:You're talking about the articles [[Imaginary number]] and [[Imaginary unit]]? The latter is about ''i'', while the former is about all numbers of the form ''b'' ''i'', where ''b'' is real. I agree that there is a lot of overlap. Does anyone else want to chime in on whether merging is warranted? [[User:Mgnbar|Mgnbar]] ([[User talk:Mgnbar|talk]]) 17:04, 17 December 2023 (UTC)

::Imaginary number refers to a [[one-dimensional space]] in the complex plane or elsewhere. A particular imaginary number is the imaginary unit which serves as a basis for the 1D space. The existence of an imaginary unit was something mysterious until the invention of linear algebra and [[matrix multiplication]]. See the Wikibook chapter [[b:Abstract Algebra/2x2 real matrices]] for representation of imaginary units.  The possible pairs i and &minus;i are found at the opposite ends of a diameter of a hyperbola. — [[User:Rgdboer|Rgdboer]] ([[User talk:Rgdboer|talk]]) 00:49, 18 December 2023 (UTC)
:Some care would need to be taken but, yes, I think these articles should be merged.  —[[User:Quantling|<span class="texhtml"><i>Q</i></span>uantling]]&nbsp;([[User talk:Quantling|talk]]&nbsp;&#124;&nbsp;[[Special:Contributions/Quantling|contribs]]) 21:59, 18 December 2023 (UTC)
::I think these two articles are about different topics (imaginary unit being about the specific value {{mvar|i}}); however, I fail to see the difference between [[imaginary number]] and [[complex number]]. I propose a merge into the latter. <span style="text-shadow: 2px 2px 8px lightskyblue, -2px -2px 8px HotPink;font-weight:bold;">[[User:Dan_Leonard|Dan]] • [[User_talk:Dan_Leonard|✉]]</span> 23:04, 18 December 2023 (UTC)
::: Imaginary numbers are those complex numbers with vanishing real part. Depending on context, an "imaginary number" might be interpreted as a [[bivector]], a quantity with the dimension/orientation of a plane and some magnitude, or as the composition of scaling with a quarter-turn rotation. In log space (i.e. a quantity to be exponentiated) an imaginary number might represent an oriented angle measure. And there are various other interpretations from there (e.g. in signal processing, electrical engineering, quantum mechanics, ...). Imaginary numbers are a type of complex number, and many of the things we might say about them are duplicative, but this kind of situation arises commonly in the encyclopedia, and in my opinion these should be separate articles. –[[user:jacobolus|jacobolus]] [[User_talk:jacobolus|(t)]] 23:33, 18 December 2023 (UTC)
:Adding a hatnote maybe can helpful? [[User:Bera678|Bera678]] ([[User talk:Bera678|talk]]) 13:54, 23 December 2023 (UTC)

::Why would you want to add a hatnote? What would you say in the hatnote?—[[User:Anita5192|Anita5192]] ([[User talk:Anita5192|talk]]) 15:41, 24 December 2023 (UTC)
:There are actually several past discussions on this topic in the imaginary unit's old discussion archives. [[User:Bera678|Bera678]] ([[User talk:Bera678|talk]]) 16:30, 28 December 2023 (UTC)

== Proof of how to use sqrt -a ==
{{Archive top|Closed per off-topic - see [[wp:Talk page guidelines]]. One can continue at [[User talk:Ulfbercht]] or somewhere else in user talk space, but please, not here. - [[User:DVdm|DVdm]] ([[User talk:DVdm|talk]]) 00:07, 3 January 2025 (UTC)}}
I submitted proof you can check on how to use sqrt -a.
no discussion or notification on the changes were made, i had to look for myself to see my edit was reverted.
Imaginary numbers are not fallacy- proof: a^2+b^2=c^2=sqrt(-c)^4=sqrt(-b)^4+sqrt(-a)^4
check and see for yourselves. ulfbercht  <!-- Template:Unsigned --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Ulfbercht|Ulfbercht]] ([[User talk:Ulfbercht#top|talk]] • [[Special:Contributions/Ulfbercht|contribs]]) 18:49, 1 January 2025 (UTC)</small> <!--Autosigned by SineBot-->

:Most content on Wikipedia needs to be supported by [[Wikipedia:Reliable sources]]. You have not cited any.
:In math articles, the policy [[WP:CALC]] gives us some leeway to include uncontroversial, easy-to-understand calculations without citing reliable sources. However, your arguments are not easy-to-understand. As a mathematician, I cannot follow them.
:So please support your contributions with reliable sources, or work to clarify your contributions before you post anything about them anywhere on Wikipedia. Regards, [[User:Mgnbar|Mgnbar]] ([[User talk:Mgnbar|talk]]) 22:59, 1 January 2025 (UTC)
::Firstly- happy new year.
::Secondly, I can provide one source for reference but after that limited research was done that i could find.
::Math typically proof is something you can check like (-a)^n=a,-a.
::As for clarification of the subject i was only today referred by a phd in physics to mathematics after he did not contradict me, i will include the necessary proof, aside from links, are drawings acceptable?
::Taken under advisement, best regards.    [[User:Ulfbercht|Ulfbercht]] ([[User talk:Ulfbercht|talk]]) 22:26, 2 January 2025 (UTC)
:::I do not understand what you are trying to say in your comment here, nor do I understand the purpose or intended meaning of your edit [[special:diff/1266636794]]. If it hadn't already been done I would also have reverted your edit as insufficiently coherent. Maybe if you link your reliable source discussing this it will be a bit clearer. Or you could try to rewrite your original comment and/or your intended technical claims for clarity. –[[user:jacobolus|jacobolus]] [[user_talk:jacobolus|(t)]] 22:33, 2 January 2025 (UTC)
:::Happy new year, Ulfbercht. On this talk page, any kind of drawing can help us understand your argument. To be accepted into the article, on the other hand, a drawing would need to be of fairly good quality.
:::Before you put much work into it, please be sure that your contribution adds something new to the article. If it rehashes the fallacy that is already present in [[Imaginary number#Square roots of negative numbers]], then maybe it's not worth the effort. Regards, [[User:Mgnbar|Mgnbar]] ([[User talk:Mgnbar|talk]]) 22:41, 2 January 2025 (UTC)
::::Ive already found what i was after:
::::https://digitalcommons.ursinus.edu/cgi/viewcontent.cgi?article=1004&context=triumphs_complex [2]
::::"We must therefore conclude, that the square root of a negative number cannot be either a
::::positive number or a negative number, since the squares of negative numbers also take the
::::sign plus: consequently, the root in question must belong to an entirely distinct species of
::::numbers; as it cannot be ranked either among positive, or negative numbers."
::::Thanks for the assistance, i have only now started to think as a mathematician, The goal is a new dimension and leading towards a new number -0, which i will happily debate once i publish a full number theory thesis. 
::::Drawings of negative roots theory I'll try to produce tomorrow. Thank you, good night.   [[User:Ulfbercht|Ulfbercht]] ([[User talk:Ulfbercht|talk]]) 22:59, 2 January 2025 (UTC)
:::::{{tq|i=yes|"a new number -0"}} – I would recommend against trying to add this kind of thing to Wikipedia, unless you are summarizing the content of reliable sources. If you are making up your own new ideas, then Wikipedia is not the appropriate venue for publishing them, see [[Wikipedia:No original research]]. –[[user:jacobolus|jacobolus]] [[user_talk:jacobolus|(t)]] 23:07, 2 January 2025 (UTC)
::::::Jacobolus is quite right to bring up Wikipedia's policy against original research. I would add that [[Wikipedia:FORUM|Wikipedia is not a forum]]. If you want to discuss your original ideas with like-minded enthusiasts, then try [https://mathoverflow.net/ Math Overflow] or some other web forum. This talk page exists solely for making improvements to the [[Imaginary number]] article based on reliable sources or routine calculations --- not original research. [[User:Mgnbar|Mgnbar]] ([[User talk:Mgnbar|talk]]) 23:25, 2 January 2025 (UTC)
::::::: That is why I had removed the entry. Closing this section before it runs out of control. - [[User:DVdm|DVdm]] ([[User talk:DVdm|talk]]) 00:07, 3 January 2025 (UTC)
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