tag:blogger.com,1999:blog-12535639.post114063760006805241..comments2021-04-02T00:42:48.223-07:00Comments on Fermat's Last Theorem: Euler's IdentityLarry Freemanhttp://www.blogger.com/profile/06906614246430481533noreply@blogger.comBlogger10125tag:blogger.com,1999:blog-12535639.post-82805142732399083502010-11-03T18:23:20.514-07:002010-11-03T18:23:20.514-07:00This is one of my favorite blogs!
Just wanted to ...This is one of my favorite blogs!<br /><br />Just wanted to let you know that there's a typo in the post:<br /><br />e^(ix) = cos x - isin x [See here for proof]<br /><br />should read: <br /><br />e^(ix) = cos x + isin x [See here for proof]Vijay Kandyhttps://www.blogger.com/profile/03393402645871744024noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-88006525125401688892009-04-30T00:03:00.000-07:002009-04-30T00:03:00.000-07:00its just a notation....dont take it in its face va...its just a notation....dont take it in its face value....e^i(theta)=cos(theta)+isin(theta)...thats it...its just a shorthand notationEULER PIPHIhttps://www.blogger.com/profile/10005296182993838143noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-23892530765630172732008-10-22T17:03:00.000-07:002008-10-22T17:03:00.000-07:00Hi llouk,Everything changes when the exponent is a...Hi llouk,<BR/><BR/>Everything changes when the exponent is an imaginary number.<BR/><BR/>You can see the details on reasoning with imaginary exponents <A HREF="http://mathrefresher.blogspot.com/2006/05/using-maclaurin-series-to-define.html" REL="nofollow">here</A>Larry Freemanhttps://www.blogger.com/profile/06906614246430481533noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-18125164962870472772008-07-01T16:26:00.000-07:002008-07-01T16:26:00.000-07:00I dont get it...How e^x=-1e is a positiv number ^x...I dont get it...How e^x=-1<BR/>e is a positiv number ^x always will give positiv...<BR/>..??lloukhttps://www.blogger.com/profile/18346832367254950918noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-53073116372726075742007-06-17T19:47:00.000-07:002007-06-17T19:47:00.000-07:00Hi Veefessional,You make the assumption that if e^...Hi Veefessional,<BR/><BR/>You make the assumption that if e^(2kπ) = 1 that 2kπ = 0.<BR/><BR/>But this is not the case as you demonstrate in the argument. In fact, the solutions to this type of equation where 2kπ ≠ 0 are called roots of unity.<BR/><BR/>A root of unity is a number that solves the following solution:<BR/>x^n = 1 where n ≠ 0.<BR/><BR/>I discuss this issue in another blog. See <A HREF="http://fermatslasttheorem.blogspot.com/2006/02/cyclotomic-integers.html" REL="nofollow">here</A><BR/><BR/>Please let me know if you have any additional questions.<BR/><BR/>Cheers,<BR/><BR/>-LarryLarry Freemanhttps://www.blogger.com/profile/06906614246430481533noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-80614103336781513452007-06-17T18:35:00.000-07:002007-06-17T18:35:00.000-07:00hmmm. i think that veefessional has a point. could...hmmm. i think that veefessional has a point. could you please post the reply on the blog? So that more people could benefit. ThanksAnonymoushttps://www.blogger.com/profile/00922177498199320235noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-61393631292124697432007-04-24T11:39:00.000-07:002007-04-24T11:39:00.000-07:00If you ask me, i itself is insanity. That it shoul...If you ask me, i itself is insanity. That it should behave so well in this identity is just amazing.Zach Merridewhttps://www.blogger.com/profile/07302294073077076878noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-1147406962497967422006-05-11T21:09:00.000-07:002006-05-11T21:09:00.000-07:00Well, what happen if you substitute x by 2π, 4π, 6...Well, what happen if you substitute x by 2π, 4π, 6π, or in general, 2kπ, where k=1,2,3,... ?<BR/><BR/>You will actually get:<BR/><BR/>2πi=0, 4πi=0 and so on, which, by dividing the constants 2 or 4 (and so on) on both sides, gives πi=o, which is inanity. What is this?<BR/><BR/>I have been thinking about it myself, you know. Haha. We share a similar wavelength range.<BR/><BR/>Do reply to me personally at Veefessional@yahoo.com.<BR/><BR/><BR/>With regards,<BR/><BR/>Vee-Liem.Veefessionalhttps://www.blogger.com/profile/01560500965752670722noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-1147196791816247332006-05-09T10:46:00.000-07:002006-05-09T10:46:00.000-07:00Ouch. That's a bad typo. I just changed it.Thank...Ouch. That's a bad typo. I just changed it.<BR/><BR/>Thanks for posting! :-)<BR/><BR/>-LarryLarry Freemanhttps://www.blogger.com/profile/06906614246430481533noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-1147192455611445182006-05-09T09:34:00.000-07:002006-05-09T09:34:00.000-07:00You don't really mean to say e = 0.552... do you??...You don't really mean to say e = 0.552... do you??Avohttps://www.blogger.com/profile/17564500396715187211noreply@blogger.com