Talk:De Moivre's Formula

1. I've always learned De Moivre's Formula as $(r( \cos \theta + i \sin \theta x))^n=r^n( \cos (n \theta) + i \sin (n \theta))$. Even though the expansion to include r is trivial, I feel we should at least mention it since it seems to me like an important part of the theorem. However, I will defer to you guys as most of you have more years of math than me.
2. On Wikipedia, typically when pages reference another page repeatedly, they only link to it the first time. Don't know what you guys think makes sense for this particular Wiki. —Cynic 23:44, 7 May 2008 (UTC)

Doesn't really matter to me, I like the wikipedia —Joe 00:00, 8 May 2008 (UTC)

I agree, that's usually the way I learned DeMoivre's Formula. However, the formulation given is equivalent to what we were taught, Joe.

$z=e^{r + i \theta} = e^r cis(\theta) \rightarrow z^n = e^{nr} (cis(\theta))^n$

and we know that

$z^n = e^{nr}(cis(n\theta))$

Thus

$(cis(\theta))^n = cis(n\theta)~{i.e.}~ e^{i(n\theta)}=cis(n\theta)$

So the statement made is equivalent.

And a quick note, I use $ cis(\theta) = \cos(\theta) + i\sin(\theta)$

Hey, sometimes this stuff displays right small, sometimes it doesn't. What's going on there? —Grambottle

For some reason, the software doesn't recoginze some things (like cis) and some things don't display properly as html and therefore are rendered as png. If you haven't already seen it, under "my preferences", there is a tab called "math" which gives you at least some control over how the mathtext is displayed.

Think we should put the expansion onto the page itself, and both clarify and make the article less stub-ish? —Cynic 22:17, 8 May 2008 (UTC)

Forced PNG and Operatorname

JA: You can append "\!" to a string to force PNG conversion, for example:

$ z^n = e^{nr}(cis(n\theta))\!$.

JA: Also, it is better semantically to use "\operatorname" for operator names, for example, $\operatorname{cis}$. This uses the right font for an operator, instead of italicizing $cis\!$ as though it were a product of three variables, $c \cdot i \cdot s$. For example:

$z^n = e^{nr}(\operatorname{cis}(n\theta))\!$.

JA: Also, with regard to redirects, it improves both internal and external search if you leave the redirects from variant search keys, for instance, De Moivre's formula and DeMoivre's Formula. Jon Awbrey 18:02, 16 October 2008 (UTC)

Not sure about the capitalisation issue, we could go on for ever and clutter the db up with all sorts of stuff. But I can see a case for DeMoivre and De Moivre even though the first is (I believe) a mistaken spelling. --Matt Westwood 19:51, 16 October 2008 (UTC)

JA: It's good to remember that the PW DB is embedded in a much bigger web, and redirects give you added search engine juice, as they say, capturing the variety of search probes that users type into their own search engines. Jon Awbrey 20:22, 16 October 2008 (UTC)

\operatorname is a new one on me, by the way, I've tended to use \mathrm for my operators. Which is shorter. --Matt Westwood 19:53, 16 October 2008 (UTC)

JA: Sure, I'm just guessing that there are LaTeX environments where \operatorname adds a semantic value to the lexical function of \mathrm. Jon Awbrey 20:22, 16 October 2008 (UTC)