設=cos2101+isin2101，求(−1)(2−1)(100−1)的值。
ans：101
請問要如何解出？謝謝！

x101=1的101個根為123100
\begin{align}   & {{x}^{101}}-1=(x-1)(x-\omega )(x-{{\omega }^{2}})\cdots (x-{{\omega }^{100}}) \\ & {{x}^{100}}+{{x}^{99}}+\cdots +x+1=(x-\omega )(x-{{\omega }^{2}})\cdots (x-{{\omega }^{100}}) \\ & 101=(1-\omega )(1-{{\omega }^{2}})\cdots (1-{{\omega }^{100}})=(\omega -1)({{\omega }^{2}}-1)\cdots ({{\omega }^{100}}-1) \\ \end{align}