Talk:Imaginary number
Talk:Imaginary number
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is this correct?[edit]
"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." Should this be "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 bi are called, respectively, the real part and the imaginary part of the complex number"? --Richardson mcphillips (talk) 16:09, 14 February 2015 (UTC)
- Most sources call b (not bi) the imaginary part of the complex number a+bi. See, for instance [1]. I have added the source ([2]). - DVdm (talk) 16:17, 14 February 2015 (UTC)
- It is correct. "bi" is not a "real" number but an imaginary number. "b" is a real number and since it's multiplied by "i" we call "b" the imaginary part. Keep in mind that the actual form is (a * 1 + b * i) where "a" and "b" are real numbers. "b" is the coefficient of the imaginary part just like "a" is the coefficient of the real part. If you describe it as a point on the complex plane "a" would be the amount on the real axis and "b" is the amount on the imaginary axis. --Bunny99s (talk) 05:46, 15 December 2016 (UTC)
Mathematical operations[edit]
Should a section on how exponentiation and square rooting is applied to these kinds of numbers be added? Gluons12 talk 20:12, 1 June 2016 (UTC).
- This seems to be already covered at Complex number#Exponentiation (where we just need to make b=0), and at Square root#Square roots of negative and complex numbers. Probably not really needed here. - DVdm (talk) 20:36, 1 June 2016 (UTC)
ALL "NON-REAL" NUMBERS ARE IMAGINARY--a + bi as well as bi--SO SAYS THE DICTIONARY![edit]
EVERY MATH TEXTBOOK I've ever read has said that "imaginary numbers" are complex numbers a + bi such that b is not zero. That is, all complex numbers other than real numbers (a) are imaginary--not just bi, which is called pure imaginary. This is also what Merriam Webster's Collegiate Dictionary, Eleventh Edition (published 2014!) says--and this is a 1,600+-page dictionary with terms ranging from tech-math like Fourier series to dirty words like fuck. Definition of imaginary number as follows (page 620):
"A complex number (as 2 + 3i) in which the coefficient of the imaginary unit is not zero--called also imaginary; compare PURE IMAGINARY"
This is a dictionary that has a lot of stuff not found in most dictionaries--and very technical-minded to boot. Besides, the idea that, within the set of complex numbers, the set of imaginary numbers represents the full complement of the set of real numbers is consistent with the other English meanings of the word "imaginary"--anything not real. If real numbers are a and imaginary numbers are only bi, what the hell are a + bi numbers called? Think about it.
I recommend that this article be rewritten, and a category/article created for "pure imaginary numbers". RobertGustafson (talk) 06:31, 15 April 2017 (UTC)
- @RobertGustafson: Different authors use different terminology. Your point is described in the last sentence of the lead:
Some authors use the term pure imaginary number to denote what is called here an imaginary number, and imaginary number to denote any complex number with non-zero imaginary part.
. Kingsindian ♝ ♚ 06:37, 15 April 2017 (UTC)
Re "unit" in 'imaginary unit'[edit]
Primarily I was confused when reading the unexplained term 'imaginary unit' in the article on complex numbers. There this term is now avoided, but substituted by a link here, where I again encountered an unexplained 'imaginary unit'. I regret that I replaced the intro sentence by something that is considered to be not de rigeur, but rebus sic stantibus, 'imaginary unit' is now again unexplained in this article, as far as 'unit' is concerned. In the talk page of complex numbers there is a thread about this question. I humbly suggest to take care about this inconsistency. Purgy (talk) 19:27, 29 October 2017 (UTC)
- The literature has no problem with the term "imaginary unit"—see Google Books. - DVdm (talk) 19:45, 29 October 2017 (UTC)
- I replied to a copy of this already in the mentioned thread. Purgy (talk) 08:27, 30 October 2017 (UTC)
first sentence[edit]
"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'?--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. --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. - DVdm (talk) 14:12, 27 May 2019 (UTC)
Hero/Heron of Alexandria[edit]
A recent edit by PaulHue was reverted by 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. JBW (talk) Formerly known as JamesBWatson 19:34, 2 October 2019 (UTC)
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