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Prove that (1+i)^n+(1-i)^n=2^((n+2)/2)....

Prove that ` (1+i)^n+(1-i)^n=2^((n+2)/2).cos((npi)/4)`, where `n` is a positive integer.

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To prove that \( (1+i)^n + (1-i)^n = 2^{(n+2)/2} \cos\left(\frac{n\pi}{4}\right) \), where \( n \) is a positive integer, we will follow these steps: ### Step 1: Rewrite the Left-Hand Side We start with the left-hand side: \[ (1+i)^n + (1-i)^n \] ...
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