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Question
For a positive integer n, find the value of `(1 - i)^n (1 - 1/i)^"n"`
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Solution
We have `(1 - i)^n (1 - 1/i)^"n"`
= `[(1 - i)(1 - 1/i)]^n`
= `[(1 - i) (1 - 1/i xx i/i)]^n`
= `[(1 - i)(1 - i/i^2)]^n`
= `[(1 - i)(1 + i)]^n` .....`[because i^2 = -1]`
= `[1 - i^2]^n`
= `[1 + 1]^"n"`
= 2n
Hence, `(1 - i)^n (1 - 1/i)^n` = 2n.
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