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![if\ i\ is\ the\ imaginary\ unit\ (i=\sqrt{-1}\Rightarrow i^2=-1):\\\\i^{97}-i=i(i^{96}-1)=i(i^{48\cdot2}-1)=i[(i^2)^{48}-1]=i[(-1)^{48}-1]\\\\=i(1-1)=i\cdot0=0\\\\therefore\ \boxed{i^{97}-i=0}](/tpl/images/0752/0095/85cc3.png)
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