#1
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$(-1)^{\frac{3*ln2}{\pi }}$ à·èҡѺà·èÒäËÃè¤ÃѺ
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âÅ¡¹ÕéªèÒ§... 03 µØÅÒ¤Á 2013 09:42 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ ¹¡¡Ðàµç¹»Ñ¡ËÅÑ¡ |
#2
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ÍÂÒ¡ÃÙééàËÁ×͹¡Ñ¹¤ÃѺ
ÃͼÙéÃÙéÁҵͺ ÇèÒáµèµÑ駶١ËÁÇ´á¹èËÃͤÃѺ |
#3
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äÁè·ÃÒº¤ÃѺÇèÒµéͧµÑé§ËÁÇ´ä˹´Õ¤ÃѺ
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#4
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$(-1)^\frac{3\ln 2}{\pi} = e^{\frac{3\ln 2}{\pi} \log(-1)} = e^{\frac{3\ln 2}{\pi}[\ln|-1| + i\cdot arg(-1)]} = e^{\frac{3\ln 2}{\pi}[0+i\cdot(2n-1)\pi]} = e^{(3\ln 2)(2n-1) i}$
$= \cos [(3\ln 2)(2n-1)] + i\cdot \sin[(3\ln 2)(2n-1)]$ àÁ×èÍ $n$ à»ç¹¨Ó¹Ç¹àµçÁã´ æ |
#5
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Íë͹֡ÍÍ¡áÅéǤÃѺ ¨ÃÔ§æ¨Ò¡·Äɯպ·¢Í§ÍÍÂàÅÍÃì¹Õèàͧ
$e^{i\theta }=cos\theta +isin\theta$ ¨Ðä´é $e^{i(2n-1)\pi }=-1 $ àÁ×èÍ $n \in \mathbb{I} $ á·¹ã¹ÊÁ¡ÒâéÒ§µé¹¡ç¨Ðä´é $ e^{(3 ln 2)(2n-1)i} $ ¢Íº¤Ø³¤ÃѺ¾Õè¡Ã |
#6
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$$\begin{array}{cl} & (-1)^{\frac{3\times ln2}{\pi }} \\ = & (e^{(2n-1)\pi i})^{\frac{3\times ln2}{\pi }} \\ = & e^{(6n-3)i\times ln2}\\ = & (e^{ln2})^{(6n-3)i}\\ = & 2^{(6n-3)i}\ ,n\in\mathbb{Z}\\ \end{array}$$
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16.7356 S 0 E 18:17:48 14/07/15 10 µØÅÒ¤Á 2013 17:24 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ Sirius |
à¤Ã×èͧÁ×ͧ͢ËÑÇ¢éÍ | ¤é¹ËÒã¹ËÑÇ¢é͹Õé |
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