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Madesmith

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複數的極式與幾何意義
Sep 13th 2013, 16:35

z=cos72度+isin72度

z^65+z^66+---+z^365
=z^65(z^301 -1)/(z -1)
=z^65(z-1)(z^300+z^299+---+z+1)/(z-1)
=z^65(z^300+z^299+---+z+1)
=1*[(z^300+--+z^296)+(z^295+---+z^291)+--
+(z^5+--+z)+1]
=1*(0+0+--+0+1)
=1*1
=1 

註:z^300+--+z^296=0 用的美弗定理
   z^365=z^65*z^(n-1) ==>n=301


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