Complex numbers exponential: Difference between revisions

Revision as of 07:04, 25 December 2006

Revision as of 09:30, 25 December 2006

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{{db|still no context to this article, so I believe this can be speedied under A1. Also, recreation of earlier speedily deleted article, so please protect}}

{{Importance|date=December 2006}}

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{{incoherent}}<!--I can't find a better tag to say "This is in jargon; please rewrite in English prose.-->

At the beginning we let take X ,Y ,z as complex numbers :-

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:<math> x^{y} = (r e^{i\theta})^{(k e^{i\varphi})} = e^{k[(\cos(\varphi) \ln(r)+ \sin(\varphi) \theta)+ i (\cos(\varphi) \theta - \sin(\varphi)\ln(r))]} \,</math>

==The Proof==

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we return y to the poler form by sub <math>A=k \cos(\varphi)</math> , <math>sub B=k \sin(\varphi)</math> . then we get....

:<math> x^{y} = (r e^{i\theta})^{(k e^{i\varphi})} = e^{k[(\cos(\varphi) \ln(r)+ \sin(\varphi) \theta)+ i (\cos(\varphi) \theta - \sin(\varphi)\ln(r))]} \,</math>