Show that `(1-i)^(n)(1-(1)/(i))^(n)=2^(n)` for all `n in N` – InterviewSolution

InterviewSolution

1.	Show that `(1-i)^(n)(1-(1)/(i))^(n)=2^(n)` for all `n in N`
Answer» `(1-(1)/(i))=((i-1))/(i)xx(i)/(i)=((i^(2)-i))/(i^(2))=((-1-i))/(-1)=(1+i)`. `therefore" ""given expression" = (1-i)^(n)xx(1+i)^(n)={(1-i)+(1+i)}^(2)=(1-i^(2))^(n)=2^(n)`.

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