If n is a positive integer, then (1+i)^ n +(1-i)^ -n is equal to :

Mathematics · JEE Main · NTA Exams — Complex Numbers and Quadratic Equations

1. \((\sqrt{2})^{n-2} \cos \left(\frac{n \pi}{4}\right)\)
2. \((\sqrt{2})^{1-2} \sin \left(\frac{n \pi}{4}\right)\)
3. \((\sqrt{2})^{n+2} \cos \left(\frac{n \pi}{4}\right)\)
4. \((\sqrt{2})^{n+2} \sin \left(\frac{n \pi}{4}\right)\)

Answer

(C) ( 2 )^ n+2 ( n 4 )

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