Simplify - 1 - i - 2 8 n - 1 - i - 2 8 n

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Relation between HCF and LCM of 3 numbers

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Question

Simplify : ${(\frac{1 + i}{\sqrt{2}})}^{8 n} + {(\frac{1 - i}{\sqrt{2}})}^{8 n}$

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{(\frac{1 + i}{\sqrt{2}})}^{8 n} - {(\frac{1 - i}{\sqrt{2}})}^{8 n} =

n \in N, {(\frac{1 + i}{\sqrt{2}})}^{8 n} + {(\frac{1 - i}{\sqrt{2}})}^{8 n} =

{(\frac{1 + i}{\sqrt{2}})}^{8 n} + {(\frac{1 - i}{\sqrt{2}})}^{8 n} =

{(\frac{1 + i}{\sqrt{2}})}^{8 n} + {(\frac{1 - i}{\sqrt{2}})}^{8 n}

n \in N

\frac{3}{1 + i} - \frac{2}{2 - i} + \frac{2}{1 - i}

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