Show that \( (1-i)^{n}\left(1-\frac{1}{i}\right)^{n}=2^{n} \) for all \( n \in N \).

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Show that \( (1-i)^{n}\left(1-\frac{1}{i}\right)^{n}=2^{n} \) for all \( n \in N \).
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