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If $i=\sqrt{-1}$ and $n$ is a positive integer, then $i^n+i^{n+1}+i^{n+2}+i^{n+3}$ is equal to
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$\begin{aligned}\text{Given,} i^n+ & i^{n+1}+i^{n+2}+i^{n+3}=i^n\left(1+i+i^2+i^3\right) \\ & =i^n\left(1+i+(-1)+\left(i^2\right) i\right) \\ & =i^n(1+i+(-1)+(-1) i) \\ & =i^n[(1+i)-(1+i)]=i^n(0)=0\end{aligned}$
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