Talk:De Moivre's formula

message: I've just edited the page in large sections but am not too familiar with wiki editing, as such my edit may seem to be laid out in a somewhat messy fashion for the < math > sections. You may also want to check the whole article to check that the tone stays constant throughout as I have not edited the entire page, only the sections that warranted it. Thank you. :) 
sumandark8600 (talk) 01:01, 17 January 2015 (UTC)
thread_title: Page might want tidying

message: Is the proof in the article the original proof of the formula? I mean, is it the way DeMoivre obtained or proved it?
Since DM's formula is a lot easier to prove using Euler's formula, I see no other reason for this proof to be in the article (except curiosity)... -- Euyyn (March 26 2005, 2346 GMT)
unreal numbers are things like -20 centimeters and the square route of -5.  —Preceding unsigned comment added by 66.189.214.66 (talk) 03:20, 5 May 2009 (UTC)
thread_title:  proof 

message: I think you guys have the parentheses in the wrong places, don't you?
cos(x+i) sin x is not the same thing as cos x + i sin x, and I'm pretty sure the latter is what you mean.  When someone who knows how to edit HTML fixes this, feel free to delete my comments here on the talk page. --anon
:You are right, there was a bug in the proof. Fixed now. Oleg Alexandrov 19:33, 3 August 2005 (UTC)
thread_title:  cos(x+i) 

message: I did a lot of formatting with the TeX and the general organization. Since I'm not an expert in the topic, I really hope I didn't mess anything up. So, if anyone who is an expert can give it a check, I'd be very grateful. Foxjwill 19:52, 5 March 2007 (UTC)
thread_title:  TeX formatting/Expert plea 

message: "The formula is important because it connects complex numbers (i stands for the imaginary unit) and trigonometry"
I think the reason for this article being so quality impaired is that it takes De Moivre's formula at face value and tries to bring together trigonometric functions and the exponential functions as if they were totally unrelated to begin with. This article reads like a formula sheet and nothing else. The real subject here is the complex exponential function, defined by the power series expansion. Sine and Cosine functions are nothing more than notational conveniences for the imaginary and real parts of said expansion, respectively.
If it weren't for De Moivre stumbling upon this before Euler's contributions, this formula would be nothing more than a novelty of Euler's formula. It would be in the best interest mathematically to merge this article into Euler's formula (because it is just that with integer-multipled arguments) or an article on complex variables but the encyclopedic standards say that it should not. I would try to improve the article but I am not versed in the art of editing. --Fusionshrimp (talk) 05:16, 22 January 2009 (UTC)
thread_title:  Complex Numbers and Trigonometry 

message: I will always recall my maths teacher explaining the wonder of de moivre who derived the following:
e to the power of pi i is equal to -1
ie: an indeterminant number to the power of another indeterminant number multiplied by an unreal number can exactly equal a negative integer.  —Preceding unsigned comment added by 58.160.121.28 (talk) 22:24, 12 February 2009 (UTC)
thread_title:  de moivre's formula 

message: Hello guys.
I m a mathematician and I want to present before you all a proof on De Moivre's theorem.Well, here is it..
Suppose n= p/q where p,q are integers and q is not equal to 0
we can write cos x + i sin x = cos (q/q)x + i sin (q/q)x
put x/q = a => cos x + i sin x = cos qa + i sin qa
=> cos x + i sin x = (cos a + i sin a)^q [using De Moivre's theorem for integers for q]
Decreasing the power by q on both sides, we have
::>>>Sorry, if you are a mathematician (as you claim), how can you "decrease the power by q"? Would you also decrease the power by 2 on both sides of the equality 2^2 = (-2)^2 ? Boris Tsirelson (talk) 19:28, 2 January 2010 (UTC)
replies: text: >>>He means take the 'q'th root of both sides. if q=2, then the square root, for example. Just like if X^2=9, then X=sqrt(9), +-3. decrease probably isn't the right way of saying it, but his maths certainly looks fine to me. 118.208.134.29 (talk) 21:47, 31 March 2010 (UTC)

text: Schaum's outline 3rd edition says the proof is outside the range of the book. The book has no proof. It states something which is wrong. The proof above is your own Original research and not based on any book. You have not raised it at WP:RD/MA for others to discuss with you like I asked nor found a published proof. Dmcq (talk) 18:55, 2 January 2010 (UTC)

text: Have a look here for why this "proof" is wrong: http://en.wikipedia.org/wiki/De_Moivre%27s_formula#Failure_for_non-integer_powers Ulner (talk) 19:11, 2 January 2010 (UTC)

text: Gosh you're quick, thanks, I was just putting in the notice that I'd raised this problem at Wikipedia talk:WikiProject Mathematics#De_Moivre's_formula. Dmcq (talk) 19:16, 2 January 2010 (UTC)

text: I've put in a couple of references to the generalization section into the leader and the bit about the failure, that deals with using fractional powers to find roots. Dmcq (talk) 09:05, 3 January 2010 (UTC)

text: What you are saying about e is only true for real powers. For complex powers e can assume any complex number value except 0. By the way greater than 0 isn't a very meaningful idea for complex numnbers. See the section Exponential function#Complex plane. See also Euler's identity which is possibly the most famous identity in mathematics. Dmcq (talk) 09:32, 3 January 2010 (UTC)

text: That was for x. No ones disputing x can be anything. The discussion is about n being a non integer value and n was taken as a half which is a rational non-integer. Dmcq (talk) 15:17, 4 January 2010 (UTC)

text: What you are saying sounds a bit similar to what I said in Talk:Exponentiation#Rational Exponents about the principal argument and rational powers if x is restricted to (-π,π]. However a person is quite entitled to specify any value they like at all for x. The business of principal argument only comes into it when converting back to angles from a sine or cosine or whatever, not when handing an argument to sine or cosine. Dmcq (talk) 10:48, 7 January 2010 (UTC)

text: Well If I would have not known that the values of sine and cosine repeat itself after a period of 2π, I would have blindly agreed with you.
But,but,but I agree a person is free to choose any thing.
But if you plot a graph of the x u have, firstly under -π,π then to 0, 2π, you would see the difference!  —Preceding unsigned comment added by Mathsislife (talk • contribs) 09:49, 8 January 2010 (UTC)

text: How about trying it with π/2 and power 5/2. If you take the square root first then you get π/4 and then the fifth power gives 5π/4. However if you take the 5th power first you get 5π/2 which is the same angle as π/2, then taking the square root gives π/4. Dmcq (talk) 20:43, 8 January 2010 (UTC)

text: Dmcq, I'd like to know where you learnt your "maths" you speak of. First off, √(1/2) = √(2/4) = √2/2; (√2/2)^5 = (√2)^5/2^5 = 4√2/32 = √2/8. Ergo: (√(π/2))^5 = (√(2π))^5/2^5 = (2π)^2√(2π)/32 = (π^2)√2π/8. (Sorry it's so long winded, I wouldn't want you to get lost somewhere, like you did in any lesson with powers). Now, in reverse: √((π/2)^5) = √(π^5/32) = √(π^5)/√32 = (π^2)√π/4√2 = (π^2)√(2π)/8  —Preceding unsigned comment added by 82.8.237.217 (talk) 18:32, 15 January 2010 (UTC)

text: Furthermore, since I forgot partway the first error I noticed, just because cos and sin have periodicity of 2π, that doesn't mean that 5π=π in EVERY branch of mathematics.  —Preceding unsigned comment added by 82.8.237.217 (talk) 18:38, 15 January 2010 (UTC)
replies: text: I'm sorry but I really can't be bothered discussing this with you any longer, you need to discuss the problems you have with complex numbers with someone who's paid for the job or likes doing it. As I said before you need to cite a book giving your argument for your argument to be taken seriously on Wikipedia.. Square roots of complex numbers have two possible values and cube roots have three etc, they do not have unique values whereas de Moivre's formula gives a single unique value. Thus it can't be true. There simply is no more to it. The generalization gives the bit about that that the value it gives is one possible value. Dmcq (talk) 18:59, 15 January 2010 (UTC)

text: No, are you paid to make it wrong? Please go and learn a bit more maths or do some cleanup where maths expertise isn't required. Peoples own work is not suitable for inclusion in Wikipedia even if it is right if it isn't cited somewhere - never mind about if it is wrong. See WP:OWN about complaining about people who defend article if you wish to complain. Dmcq (talk) 17:28, 21 January 2010 (UTC)

text: If some editors disagree about an  article and there seems no way for them to resolve the dispute on their own then they should follow the WP:DISPUTE process rather than continuing. I asked at the maths wikiproject for other people to look at it and they agreed with me. You still disagree and I see little prospect of agreement. I was pointing out to you the route to complain about me if you felt I was guarding the article from people correcting it. Please read the dispute policy. You can either ignore this article, raise an action yourself, or change the article and have me raise an action. Dmcq (talk) 09:05, 5 February 2010 (UTC)
thread_title:  Proof for n belonging to the set of Rational numbers! 

message: The section titled "De_Moivre's_formula#Formulas_for_cosine_and_sine_individually" gives a formula for cos(nx) that assumes "n" is even.  Likewise, it gives a formula for sin(nx) that assumes "n" is odd.  The correct formulae that don't make these unwarranted assumptions are here.  I will fix.Anythingyouwant (talk) 05:10, 27 August 2011 (UTC)
replies: text: As far as I can see the old formulae were correct and the new ones are also correct. I can't say I'm particularly happy with either. Neither are very obvious from the original formula. However the new one seems a bit worse to me as having a funny construction for generating just one or minus one and removing half the entries. I've put a new version at here which should make the correspondence more obvious. Dmcq (talk) 11:37, 27 August 2011 (UTC)
replies: text: I've commented over there at List of trigononetric identities.  I think it would be better to just add a sentence about the effect of the sine function.  I'll try that in this article.Anythingyouwant (talk) 16:41, 27 August 2011 (UTC)
thread_title: Unwarranted assumptions about whether "n" is odd or even

message: Allegedly, the Abramowitz and Stegun Handbook of Mathematical Functions was used to source this article.  Yet, the source only contains 3 lines about De Moivre's formula.  This material says that if x is restricted to a 360° range, then n can be any number; if the restriction is not made, then n must be taken as an integer.  This does not agree with the Wikipedia article's presentation of the subject. For that reason I am encouraging editors to find more citations for this article. Thelema418 (talk) 17:16, 19 August 2012 (UTC)
thread_title:  Refernces, etc. 

message: This formula is named after Abraham de Moivre in which I assert that it should be properly titled de Moivre's formula (lowercase title) as opposed to De Moivre's formula as the formula is not named after Abraham De Moivre. Technical 13 (talk) 18:10, 19 May 2013 (UTC)
replies: text: Here is a correctly capitalized sentence: "De Moivre's formula does not, in general, hold for non-integer powers."  The title "De Moivre's formula" is correctly capitalized for the same reasons the sentence is correctly capitalized.  On the other hand, the two capital "D"s bolded in the first sentence should be lower-cased.  --JBL (talk) 18:36, 19 May 2013 (UTC)
replies: text:  The exception here is that fact that his name is "de Moivre" and it does not matter where it comes in the sentence since it is a noun.  You wouldn't say "EBay's auctions are final." or "IPod's sales are in the multi-millions." It would still be "eBay's auctions are final." or "iPod's sales are in the multi-millions." respectively. So, considering it is a proper noun no different than the other two examples, I maintain that the article should be  and that any usage of it would be properly represented as "de Moivre's formula does not, in general, hold for non-integer powers." Technical 13 (talk) 18:52, 19 May 2013 (UTC)

text:  WP:NAMECAPS supersedes personal names and specifies: "Proper names of specific places, persons, terms, etc. are capitalized in accordance with standard usage: Winston Churchill, John de Balliol, Wales, Tel Aviv, Three Great Gardens of Japan, etc." Based on that, I maintain that the article should use the  template regardless of how it is linked to from other articles. Technical 13 (talk) 21:21, 19 May 2013 (UTC)

text:  Okay, had to save to go find the diff...  when  added  here. Technical 13 (talk) 21:25, 19 May 2013 (UTC)
replies: text: I would maintain that "standard usage" in this case is to use the capital letter when the name appears at the beginning of a sentence (although not, of course, elsewhere), and see no statement that NAMECAPS "supersedes" the rest of MOSCAPS. Indeed, NAMECAPS doesn't mention the specific circumstance questioned here, while, elsewhere in the same article in which it appears, there is a specific statement to the effect that it doesn't apply in this situation. Although I obviously don't have the final word on this, IMO, the specific guideline would supersede the more general one. Otherwise, why have it? Anaxial (talk) 22:00, 19 May 2013 (UTC)
replies: text:  That is exactly my argument, the policy supersedes the general usage page. The only question here is whether or not the article should have the  template exactly the same as this talk page has as was instituted by an administrator/oversighter/arbitrator. Technical 13 (talk) 22:29, 19 May 2013 (UTC)

text: I'm not sure that we on the same page.  It doesn't matter where it comes in the sentence. The article should be de Moivre's formula with the  just like an administrator/oversighter/arbitrator  almost three years ago.  Technical 13 (talk) 23:59, 19 May 2013 (UTC)
replies: text: That would be true if and only if it is standard to treat capitalization in French names in this way.  Do you have any evidence at all to support the idea that this sort of nonstandard capitalization is used anywhere, by anyone?  JBL (talk) 00:55, 20 May 2013 (UTC)
replies: text:  So, you want an WP:OTHERSTUFFEXISTS list?
* de Bie
* de Blob
* de Blob 2
* de Buddy's
* de Bourdeille
* de Branges's theorem
Hey, there we go... Another mathematical thing exactly as in this instance that uses  just like I think this article should... There is your standard to treat capitalization for French names that are used as proper names for mathematical formulas and theorems in this way. I hope this satisfies your request. Technical 13 (talk) 01:18, 20 May 2013 (UTC)
thread_title:  Abraham de Moivre's formula 

message: The "x" is NOT a complex number. It is the angle of the vector representing the actual complex number, which is "r*(cos(x)+i*sin(x)". An important part of De Moivres formula is "r" which is the length of the vector, because without "r" only complex numbers with numerical value of 1 are represented, and the formula holds for ANY complex number. 87.52.19.19 (talk) 19:07, 17 May 2018 (UTC)
replies: text: This is a difficult one. The statement in the lead is actually true, sine and cosine have been extended so they are defined for complex numbers. However using complex numbers instead of reals in this context is unusual, and especially in elementary maths. De Moive certainly wouldn't have meant complex numbers. I think the mention of x possibly being  a complex number should be removed from the lead and x just called an angle, and x possibley being complex should just be mentioned as an extension in the article. Dmcq (talk) 22:38, 17 May 2018 (UTC)
replies: text:  This would be ok with me.  This only addresses one of the two issues IP raised; the other one (about adding r) is less interesting. --JBL (talk) 23:29, 17 May 2018 (UTC)
replies: text: Good to hear both a clarification and an agreement. Must admit I didn't know of, nor consider the possibility of complex angles. I would still insist on adding "r", because it is both an essential part of De Moivres formula and an absolute necessity for the notifcation of complex numbers in polar form. 87.52.19.19 (talk) 17:28, 18 May 2018 (UTC)
thread_title:  This is not true 

message: Can this equality be used in an elementary proof of Euler's formula, at least in the logarithmic form obtained by Roger Cotes?--109.166.134.178 (talk) 18:19, 22 April 2019 (UTC)
replies: text: You'd need to approximate and go to limits, I don't think that would be elementary. Dmcq (talk) 18:34, 22 April 2019 (UTC)
thread_title:  Use in the proof of Euler's formula