Talk:Complex number/Archive 1

message: I could not find Demovire's theorem for complex numbers,should add this.-Raj.B (India-Karnataka-Mysore) —The preceding comment was added on 06:33, 13 December 2003.
:It's at De Moivre's formula. I've put a link to it in the article. --Zundark 10:18, 13 Dec 2003 (UTC)
thread_title:  De Moivre's formula 

message: everything fine there in the article. as an encyclopeadian article. but shouldn't there be exercises?
--jai 12:20, Aug 13, 2004 (UTC)
:No. An encyclopedia isn't a problem-solving book. But wikibooks... That idea would fit right in. --Mecanismo 10:07, 16 September 2005 (UTC)
thread_title:  Exercise Needed 

message: 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. —The preceding unsigned comment was added by Borb (talk • contribs) 12:38, 24 May 2005.
Engineers tend to use j, and mathematicians i.
Robinh 13:52, 24 May 2005 (UTC)
thread_title:  j or i - usage of the imag. unit in maths, physics, electrotechnology 

message: The article says:
::The field C is (up to field isomorphism) characterized by the following three facts:
::* its characteristic is 0
::* its transcendence degree over the prime field is the cardinality of the continuum
::* it is algebraically closed
OK, so one adds a set of transcendental elements of cardinality c.  If one adds only a proper subset of those, with the same cardinality, does one get a proper subfield?  Does C therefore have proper subfields isomorphic to C?  If so, one gets an infinite descending chain of proper subfields isomorphic to C, and their intersection is also a subfield; what does it look like? Michael Hardy 00:14, 3 August 2005 (UTC)
replies: text: If you add a proper subset the algebra might change such that you end up with C no matter what. --MarSch 15:44, 8 September 2005 (UTC)
thread_title: Algebraic characterization

message: Alas the subject of 'complex numbers' is made advanced from the beginning. Consider the geometric plane of points. Choose a zero point, 0, and a unit point, 1. If the triangle (0,A,X) is similar congruent to triangle (X,B,0), then X=A+B. If the triangle (0,1,A) is similar to triangle (0,B,X), then X=AB. This definition of addition and multiplication of points in the plane is nice to the beginner who only needs to know the geometric concept of similar triangles, but no knowledge of real numbers is needed. Complex numbers are easier than real numbers. 
Bo Jacoby 07:40, 8 September 2005 (UTC)
replies: text: this is a nice alternative definition, but whether it is simpler is debatable. --MarSch 15:49, 8 September 2005 (UTC)
replies: text: Feynman used it in QED, and it should be at least included. Septentrionalis 17:01, 9 September 2005 (UTC)
thread_title:  Elementary geometry 

message: If z=x+iy where x and y are real, then x is the real part and iy is the imaginary part. y is neither imaginary nor a part. Why do you call y the imaginary part ? Bo Jacoby 12:49, 20 September 2005 (UTC)
replies: text: This is the standard def for the imaginary part. Im(x+iy):=y. It is projection onto the second coordinate. --MarSch 17:40, 25 September 2005 (UTC)

text: No, C is R^2 with the product (a, b)(c, d) = (ac - bd, ac + bd). Then you can make the definition i := (0, 1). Thus x + iy = (x, y) and if you project to the second coordinate you get y. i is just a basis vector. --MarSch 13:07, 28 September 2005 (UTC)

text: F(F(x+iy))=F(y)=F(y+i0)=0 \ne y=F(x+iy) 
while P(P(x+iy))=P(iy)=iy=P(x+iy).
So  FF \ne F while PP=P.
F is not idempotent. P is idempotent.  Bo Jacoby 08:17, 29 September 2005 (UTC)
thread_title:  The imaginary part 

message: The Geometry section should be deleted, or at least rewritten so that it makes some kind of sense. The article begins with a nice definition of complex numbers and continues with discussions of complex numbers as coordinates, which are arguably the two most common definitions but stuck in the middle is this incoherent rigamarole discussing similar triangles. The article is intended to serve as an encyclopedia article, not a pedagogical tool (again, assuming the Geometry section is teaching anyone anything).
The section is so egregiously bad I was tempted to just delete it without consultation, but there seems to be some who think it has some value. Please show me what that value might be.--andersonpd 01:28, 21 October 2005 (UTC)
replies: text: I don't much like that section either, it is rather badly written and does not seem to be extremely relevant. There is some text above it explaining the complex plane and polar coordinates, that should be enough. If somebody has the energy to write a nice Geometry of complex numbers article to explain in more coherent way the stuff in that section, it would be good. Otherwise, bring the axe brother. Oleg Alexandrov (talk) 04:43, 21 October 2005 (UTC)

text: Would you be willing to move the "Geometry" section to a new article? That material is of course related to complex numbers, but it is more like an application (and not a really important one). As such, it was not right to put it before other, more immeadiate properties of complex numbers, like division, absolute values, etc. I think that section is not even as relevant as the sections now below it, which are "Solutions of polynomials equations", "Algebraic characterizations", etc. And by the way, the "Geometry" section is indeed not well written. Oleg Alexandrov (talk) 08:48, 21 October 2005 (UTC)

text: Geometry means pictures, sir. I found the formulas in there hard to follow. Several pictures, and replacing all those triangle symbols plain words, say caption to the pictures, would go a long way towards improving that section. Also, it needs to be made shorter. There is no need to rederive again the complex numbers, with X^2+1 and all that. What is needed is a rather short section explaining how addition, multiplication and conjugation would look like in geometric terms. Oleg Alexandrov (talk) 09:43, 21 October 2005 (UTC)
replies: text: The geometric view is just another way of defining the complex numbers and as such should be in this article. Pictures would definitely improve it a lot, but that is no reason to delete what's there now. What I don't understand yet is how the plane is defined if you don't use real numbers. I mean you can't say, the plane is R^2, so what do you say? --MarSch 11:08, 21 October 2005 (UTC)
thread_title: Geometry?

message: (The subsection grew, so I make a new header here.) I agree completely that pictures will improve it, but alas I'm no good at drawing. We need (1) an addition picture showing by similar triangles (0,1,1+i) and (2+i,i,1) that (1+(1+i)=2+i); (2) a multiplication picture showing by similar triangles (0,1,1+i) and (0,2i,-2+2i) that (1+i)(2i)=-2+2i; (3) a conjugation picture showing by mirror triangles (0,1,2+i) and (0,1,2-i) that (2+i)*=(2-i), and (4) an i picture showing by similar triangles (0,1,i) and (0,i,-1) that ii=-1. The plane was defined by Euclid many hundred years before real numbers were invented. Bo Jacoby 12:47, 21 October 2005 (UTC)
replies: text: I can take care of the pictures, in the next several days. Bo, one important thing which I also said earlier is I believe you got a bit carried away in that section. There is no need to talk about the factorization of X^2+1 and all that stuff below it. This is one of those cases in which putting more information does not help, but rather confuses the reader. If you do want to elaborate, you should I think start a new article, and keep here only the important points. Oleg Alexandrov (talk)13:49, 21 October 2005 (UTC)
replies: text: I believe that moving the geometry info to its own section has improved the overall flow of the article. I concur that adding pictures would be a great help in making the geometric definition clear. And I agree that a separate article would be a good way to cover the information in depth. In fact, I think that's probably the basis for my original objection -- the subject was presented without any transition or explanation of its purpose or goal. It is an interesting sidelight, but it is, IMHO, only that -- a sidelight. (unsigned post by Paul D. Anderson, 10:35, 21 October 2005).
Thank you, gentlemen. Your objections has so far lead to a substantial improvement, which is what this is all about. I wondered why elementary 'complex' number theory assume advanced stuff like  trigonometry, exponentials and vectors, and what is the square root of minus one? The geometrical approach shows why ii=-1. No big deal, just similar triangles. One guy's sidelight is another guy's mainlight. As to the factorization of polynomials: it would be nice to have a bridge between geometry and algebra instead of separate islands. The points of intersection between circles and lines are the roots of a polynomial, leading to the factorization of the polynomial. This insight motivate the study of factorizations. Bo Jacoby 16:55, 23 October 2005 (UTC)
thread_title: Elementary geometry

message: I am a high school student who excels in math. However I do not completely understand the meaning behind complex numbers.  Why is it that  ln(-1)=(pi)x(i)
What is its application or real world significance?-nick
:Hi Nick ! ln(−1) is a solution to ex = −1. No real number x satisfy this equation. If x = it is an imaginary number, then ex = eit is a point on the unit circle. See Exponentiation#Powers_of_one. t is the length of the arc along the circle from point 1 ( = 1 + 0i) to eit. When you have walked the length π along the unit circle starting at 1, then you have arrived at the point −1 ( = −1 + 0i). So eiπ = −1. And so ln(−1)=iπ. Keep asking ! Bo Jacoby 09:53, 3 November 2005 (UTC)
replies: text: Hi Nick, I recommend you check out a text or course on complex analysis.  If you like math, then you'll probably enjoy the opportunity to re-derive many of the rules you know from real numbers but with complex numbers.  I took complex analysis in college and see no reason sharp high school students couldn't manage the material (with the possible exception of some of the calculus that only a few high school students have learned).  I used an out of print book from the seventies and Schaum's.  I recommend the latter.  Cheers - --rs2 17:17, 5 November 2005 (UTC)
thread_title:  ln(-1) 

message: I need input on what is or has a consensus for being the correct symbol for the real part of a number and the imaginary part. I have seen someplaces using Black Forest \mathfrak{R I}. I'm thinking blackboard \mathbb{R I} is appropriate or even calligraphy \mathcal{R I}. I don't want to wreck a few pages and then find out I was wrong. Snafflekid 06:19, 10 November 2005 (UTC)
replies: text: I don't think there is any universal consensus on font, but blackboard \mathbb{R} is often used to signify the set of real numbers. The real part function is not used as much as the complex conjugate function. Many authors do without it, and so the problem is solved. Bo Jacoby 07:29, 10 November 2005 (UTC)
replies: text: I agree that \mathbb{R} is not suitable, but I think that the functions can be useful. As notations simply Re(z) and Im(z) are fine too.--Patrick 12:24, 10 November 2005 (UTC)
replies: text:  Agree with Patrick that Re and Im are good enough. Some people use \Re and \Im, written as \Re and \Im, but I am not sure it is worth it. Oleg Alexandrov (talk) 19:29, 10 November 2005 (UTC)

text: I have reviewed my books and textbooks by various lettered and sundry authors. There seems to be a 3:1 ratio of \mathcal{R}{e}(z)  \mathcal{I}{m}(z) to Re(z) Im(z). I recall all my professors writing the function using script as well. But I'm an electrical engineer and this function comes up a lot in discussing phasor notation. Selection bias? Snafflekid 19:37, 10 November 2005 (UTC)

text: Put me in the Re(z) and Im(z) camp. Maybe my age is showing, but I've never seen either the script or Black Forest versions.--andersonpd 20:26, 10 November 2005 (UTC)
replies: text:  One reason to stick with the simpler Re and Im instead of fancy fonts is that fancy fonts will become images, and will look out of proportion when embedded in text. Plain text is preferrable to PNG images, as per the math style manual. Books are written on paper and don't have this issue. Oleg Alexandrov (talk) 01:04, 11 November 2005 (UTC)

text: Plain text looks fine, I think, but that doesn't help if LATeX is being used. I found a page using \operatorname{Re}(z) typed as \operatorname{Re}(z). Very clean IMO. Plain text will be italicized otherwise and that is definitely wrong. Snafflekid 02:05, 11 November 2005 (UTC)
thread_title:  correct symbol? 

message: Fiedorow's large section on history is well written! But is it well placed too? Are there general WP articles on the history of mathematics to refer to or to be referred to? Bo Jacoby 08:00, 7 December 2005 (UTC)
thread_title:  History 

message: My revert was caused by rather clumsy recent writing, and an unnecessary example of complex number multiplication. This is an introduction after all, not the whole article, so need to be kept short and consise. The issue of multiplication is dealt with very cleary right below the table of contents. Oleg Alexandrov (talk) 04:53, 21 February 2006 (UTC)
thread_title:  My reversion 

message: I rather prefer a clumsy but didactical and correct text, over a conc(!)ise, incorrect and less comprehensive one. Almost always in introductory texts on complex numbers somewhere the frase "square root" of -1 turn up. Is it meant to shock the reader and implicitly implying the author isn't? In introducing the complex numbers the square root is not yet defined.Nijdam 23:54, 22 February 2006 (UTC)
replies: text: The issue of what is i is dealt with at length below. Oleg Alexandrov (talk) 03:40, 23 February 2006 (UTC)
replies: text: Quite a lenghty discussion! And so it should be! Then what is i??Nijdam 15:57, 17 March 2006 (UTC)
replies: text:  Well, i is the number (0, 1) in the plane, which squared, by the rules of complex numbers, give (-1, 0), that is, -1. You are right that something more must be said about i, as it was mystifying people for a long time, but I don't find the intro appropriate for that. The text you want, about what is i,  already exists at Imaginary unit, and that one is linked form the intro. Oleg Alexandrov (talk) 01:50, 18 March 2006 (UTC)
replies: text: Well It wasn't a question from my side. I know what i is and what it is not. I would never say i is the point (0,1) ...It may be defined that way, with the complications of the embedding of the reals. It may be defined otherwise, like the historical way, or as a matrix.Nijdam 10:58, 30 April 2006 (UTC)
thread_title: Clumsy

message: There is a redirect from Complex line the this entry. But I cannot find it picked up somewhere. Is there space left to integrate this into this article? Hottiger 18:43, 21 March 2006 (UTC)
replies: text: Well, complex line is described here. I don't think that should redirect to this article, for that reason I will now delete that redirect. Oleg Alexandrov (talk) 04:13, 22 March 2006 (UTC)
replies: text:  OK, one may think of the complex line as C viewed as vector space or manifold over itself. But I don't think that terminology is used that much. Oleg Alexandrov (talk) 04:27, 22 March 2006 (UTC)
thread_title:  Complex line 

message: I know these are easy to prove but as a reference it is easier to just look up these values then to have to prove it every time. These also provide and way to work backwards in proofs since it gives a hint to the answer.
\sqrt i={\frac{1+i}{\sqrt2}},\mathbf{i^2}=-1,\mathbf{i^3}=-i,\mathbf{i^4}= 1Adhanali 03:04, 4 April 2006 (UTC)
replies: text: Yeah, but this is a big article, and including a lot of various miscellaneous  formulas make it overall harder to read. That is, at some point one needs to decide what to include and what to skip when writing something, and, at least in my view, these identities are not worth having in. Oleg Alexandrov (talk) 03:06, 4 April 2006 (UTC)
replies: text: Is there any place where we can put \sqrt i={\frac{1+i}{\sqrt2}}. Even if it is not on this page. I am not sure about others but it is not a common identity I run into often and when I need to use it I can never remember it. I just thought it might be useful. But I understand the length versus content issue. Cheers Adhanali 03:28, 4 April 2006 (UTC)
replies: text: Special case of Euler's formula for eiπ/4? Septentrionalis 05:46, 4 April 2006 (UTC)
replies: text:  puting root i in... lol u mean helping ppl do their homework?
The formula may belong in the article root of unity. Bo Jacoby 07:52, 3 May 2006 (UTC)
thread_title:  Identities 

message: Why does the page polar form redirect here? The word polar isn't even in the article. Fresheneesz 05:06, 26 April 2006 (UTC)
replies: text: Polar form is another way of writing complex numbers, when written in the form a + bi, the are said to be in rectangular form. When in the form of r cis \vartheta it is said to be in polar form.--Phoenix715 08:59, 16 June 2006 (UTC)
replies: text: Polar forms also exist e.g. for quaternions (e.g. K. Carmody, Circular and hyperbolic quaternions, octonions, and sedenions, Appl. Math. Comput. 28 (1988) 47–72. doi:10.1016/0096-3003(88)90133-6) and other numbers. Let me look around and make sure that "polar form" is defined as an expression using angles and one (absolute) length (distance to origin / zero). A quick internet search indeed returned only complex numbers expressed in polar form, so a new article here with more examples should be interesting, and I'd be glad to write it up. Through polar coordinates, it would give a geometrical viewpoint on multiplication on some hypercomplex numbers, next to the rectangular / Cartesian product. Any comments are always welcome. Thanks, Jens Koeplinger 13:46, 31 July 2006 (UTC)
replies: text: I am puzzled by the fact that we seem to be using polar and geometrical synonymously, as if rectangular/Cartesian representation is not geometrical.  Polar representation makes multiplication easier but addition much harder.  Are we implying that multiplication is more geometrical than addition?  --Bob K 19:56, 31 July 2006 (UTC)
replies: text: Thanks for pointing out this wording inconsistency. Rectangular / Cartesian coordinates are just as "geometrical" as polar forms / coordinates. I should really have said an "additional geometrical viewpoint" or so. From my end, this mishap came from an abstract algebra mindset, creating algebras by demanding certain abstract properties (distributivity, associativity, commutativity, etc). But of course, this cannot be separated from geometry. I'll check my edits and make sure to eliminate this incorrect wording if I find it. Thanks, Jens Koeplinger 22:04, 31 July 2006 (UTC)
thread_title:  polar form 

message: This page seems a bit disorganized to me. For example, all those things under the header "definitions" don't seem to be definitions. They're not definitions of "complex number" in any case. I think this page should have a header called "properties" that includes indenties, and other properties of complex numbers - instead of having the properties strewn all over the place. 
Perhaps a "representation of complex numbers" section would be good to place the matrix representation and vector representation, along with the complex plane and the complex number field. As it stands, the TOC is long and this page is hard to sift through to find what you need. Fresheneesz 04:07, 19 May 2006 (UTC)
replies: text: Agreed, organization was the main reason I rated the article as B-class. I'll take a look and see if we can get the ToC trimmed a bit. --JaimeLesMaths 03:37, 6 October 2006 (UTC)
thread_title:  Organization or... not? 

message: I'm not sure how to edit this, but perhaps there needs to be revision of the sentence "when b=0, then this is just the real number a" (not verbatim)
The real number a is actually a complex number a+0i. For non mathematicians, this is not just being petty this is involved with a fundamental definition in algebra that the complex numbers provide the solutions to all equations etc. I can't think how better to word it though, so perhaps someone with better linguistic skills could give it a go?
Triangl 12:38, 19 December 2006 (UTC)
replies: text: I changed the sentence to "We usually identify the real number a with the complex number a+0i.". Does that satisfy you? JRSpriggs 08:22, 20 December 2006 (UTC)
thread_title:  When Im(z)=0 

message: I was wondering if perhaps the "Polar form" section could be made shorter, and with most of the material moved to its own article, called Polar form. Then, at the top of the current section "Polar form" in this article we could point to the article Polar form for more details. Would that be a good idea? Oleg Alexandrov (talk) 17:00, 29 December 2006 (UTC)
replies: text: Yes it is a good idea.  But I also think that the link to the 17-gon is a good idea. Gauss' use of complex numbers for analyzing the 17-gon was a historic breakthrough, and your edit comment: "This section is about geometric interpretation of algebraic stuff, and not the other way around", is a misunderstanding. Bo Jacoby 12:46, 30 December 2006 (UTC)

text: I don't think that this is a good idea, because the polar form seems to be a basic of the complex number article. However, perhaps some details on calculating the argument when converting from Cartesian to polar form could be moved to Polar coordinate system, but that article is already a bit too long in my opinion. Perhaps the section on complex numbers in that article could be merged-in here. --IP 18:56, 30 December 2006 (UTC)

text: The article on polar coordinates contains the information that now pollutes the article on complex number. Bo Jacoby 16:40, 1 January 2007 (UTC)
replies: text: Sorry, but that's currently not correct. The article on polar coordinates does not contain a formula to calcuate the angular coordinate in the interval (-π, π] as it is usual for complex numbers. I had added this, but it was deleted again. --IP 02:34, 2 January 2007 (UTC)

text: Polar_coordinate_system#Converting_between_polar_and_Cartesian_coordinates contains formulae for the requested calculation. I think we should link to that article and not include the formulae here.Bo Jacoby 23:20, 11 January 2007 (UTC)
thread_title:  Polar form 

message: I've been re-reading this article, looking for ways it might be improved, and one thing keeps grabbing my attention. The two sections "Notation and operations" and "The complex number field" are very repetitive. I think we should either separate some of these ideas and only state them once, in one section or the other, or else we should merge these two sections into a single section, perhaps with a new title. What do you think?  DavidCBryant 23:22, 24 January 2007 (UTC)
replies: text: That is more about set theory than complex numbers per se. It should be mentioned, but in a different article. JRSpriggs 07:41, 26 January 2007 (UTC)
thread_title:  Department of redundancy department 

message: The section "Absolute value, conjugation, and distance" contains the sentence, "The addition, subtraction, multiplication and division of complex numbers are then continuous operations." First, I've never heard of a "continuous operation" (though I think I understand what the sentence was trying to get at), and second, the sentence does not seem to add anything to the paragraph it's in. I'm removing it for now, but, if you think it should be retained, a rephrasing is probably in order first. I'm happy to talk through it with anyone who wants to take a crack at it. --JaimeLesMaths (talk!edits) 10:41, 26 January 2007 (UTC)
replies: text: These "operations" are just functions of two variables. Of course, continuity makes sense for them. JRSpriggs 11:38, 26 January 2007 (UTC)
replies: text: OK, well, yes, the operations are continuous functions from C x C to C, not from C to C (which is what I thought was meant and was why I was confused). Thus, I don't think the sentence is relevant to the paragraph and will only add confusion. --JaimeLesMaths (talk!edits) 04:36, 27 January 2007 (UTC)
thread_title:  Continuous operations? 

message: I noticed that someone has added "root extraction" to the list of operations "addition, multiplication, and exponentiation in polar form". While I was doing some minor mopping up after that, I also noticed that somebody, I don't know who, has very carefully miscoded the exponential function as
:\mathrm{e}^z\,
instead of using the standard (universally accepted, I think) notation
:e^z.\,
So now I'm reverting that to standard notation, and I'm leaving a note here just in case someone objects.  DavidCBryant 16:43, 26 February 2007 (UTC)
thread_title:  Notation 

message: In EE the notation preferred is A+jB as opposed to A+Bj. —The preceding unsigned comment was added by Streyeder (talk • contribs) 15:18, 2 March 2007 (UTC)
thread_title:  Electrical Engineering 

message: ok look, im a high schooler doing some research on various topics concerning complex numbers and im having a really hard time trying to understand most of the information in this article.  Anyone know any place where complex numbers may be easily comprehended? thanks.76.18.202.211 18:48, 22 April 2007 (UTC)
replies: text: If you could give some examples of things in this article that aren't easy to understand, then maybe someone could improve the explanations. --Zundark 19:07, 22 April 2007 (UTC)
thread_title:  wow 

message: isn't the square root of a negative number -|x²| —The preceding unsigned comment was added by 24.187.129.93 (talk) 21:27, 25 April 2007 (UTC)
replies: text: No, it isn't. Every real number, when squared, gives a positive result, because (−1)2 = +1. That is why every positive real number has two square roots (a positive root, and a negative root). To represent the square root of a negative real number we must use the imaginary unit i.  DavidCBryant 21:49, 25 April 2007 (UTC)
thread_title:  square of a negative number 

message: The present table of contents of section 1 is:
1 Definitions
:1.1 Equality
:1.2 Notation and operations
:1.3 The field of complex numbers
:1.4 The complex plane
::1.4.1 Polar form
::1.4.2 Conversion from the polar form to the Cartesian form
::1.4.3 Conversion from the Cartesian form to the polar form
::1.4.4 Notation of the polar form
::1.4.5 Multiplication, division, exponentiation, and root extraction in the polar form
:1.5 Absolute value, conjugation and distance
:1.6 Complex fractions
:1.7 Matrix representation of complex numbers
I suggest that sections 1.4 and 1.7 be moved elsewhere, as they go beyond basic definitions. 
Bo Jacoby 15:39, 20 July 2007 (UTC)
thread_title:  The section on definitions should mainly contain definitions.  

message: References section contains dead link: http://people.bath.ac.uk/aab20/complexnumbers.html Dan Kruchinin 22:41, 23 October 2007 (UTC)
thread_title:  Dead references 

message: Polar interpretations of complex numbers and their mathematics can be very intuitive. Why is the discussion of complex math in polar coordinates separated by section from the rectangular coordinate interpretation? Also, the discussion of polar vs. Cartesian coordinates happens early, but is not expanded until deep in the article. 
Awesome results like "multiplication corresponds to multiplying their magnitudes and adding their arguments" are buried at the end of a discussion of the coordinate system, but do not appear in the multiplication section. Finally, an interpretation of sinusoids with complex numbers in polar form is not covered in anyway but the driest mathematical description of Euler's formula. The interpretation of sinusoids as projections of circles onto lines should make it's way into this article somehow.  — Preceding unsigned comment added by OceanEngineerRI (talk • contribs) 18:55, 12 September 2013 (UTC)
thread_title:  Very awkward discussion of polar coordinates 

message: Is it? I don't think it is necessarily. Cause if i=sqrt-(1) then i*i=sqrt-(1)*sqrt-(1)=sqrt(-1*-1)=sqrt(1)=1
Which we know isn't true since i^2=-1 not 1. — Preceding unsigned comment added by Fipplet (talk • contribs) 
: You have made a common mistake. See Imaginary unit#Proper use for one explanation. --JohnBlackburnewordsdeeds 13:41, 31 January 2012 (UTC)
replies: text: The principal value of sqrt(-1) is defied to be i rather than −i so yes they are the same. There is no requirement though that the principal value of square root the product be equal to the product of the principal values of the square roots, there are two possible square roots and it so happens that you should have taken the negative square root in the last step above. And in fact if a second square root of -1 occurs there is no guarantee without extra checks that it will be i if i already occurs. This is a bit like if you have x2=1 and y2=1 the possible values of x+y are −2, 0, and 2. Dmcq (talk) 15:56, 31 January 2012 (UTC)
replies: text:  Good explanation. Themekenter (talk) 02:52, 1 December 2013 (UTC)
thread_title:  i=/=sqrt-(1) 

message: This edit makes the implication that ordering is an algebraic property.  It has the feel of WP:OR about it, but I do not have the knowledge to be sure.  I'll leave it to others to decide and possibly fix this.  —Quondum 13:56, 13 March 2014 (UTC)
replies: text: Replacing "the algebraic properties" by "the properties" fixes the problem.  MvH (talk) 13:46, 10 April 2014 (UTC)
thread_title:  Is ordering considered to be an algebraic property?