Prove that \( i^{n}+i^{n+1}+i^{n+2}+i^{n+3}=0 \), for all \( n \in ...

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Prove that \( i^{n}+i^{n+1}+i^{n+2}+i^{n+3}=0 \), for all \( n \in \mathbf{N} \).
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