回復 1# mandy 的帖子
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\( f(x)=\frac{x^{100}+x^{99}+\cdots +x+1+z}{x^{101}-1+1} \)
\( =\frac{x^{100}+x^{99}+\cdots +x+1+z}{(x-1)(x^{100}+x^{99}+\cdots +x+1)+1} \)
令 \( g(x)=x^{100}+x^{99}+\cdots +x+1 \)
所以,\( f(1+\bar{z})=\frac{g(1+\bar{z})+z}{\bar{z}g(1+\bar{z})+1}=z=cos\frac{2\pi }{17}+i sin\frac{2\pi }{17} \)
[ 本帖最後由 lianger 於 2012-6-23 02:21 PM 編輯 ]