If n is a positive integer,then (1+i sqrt{3}) | vedclass

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(C) Let $z = 1 \pm i \sqrt{3}$. We can write $z$ in polar form as $2(\cos \frac{\pi}{3} \pm i \sin \frac{\pi}{3})$.Then,$(1+i \sqrt{3})^n + (1-i \sqrt

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$2^{n+1} \cos \frac{n \pi}{3}$

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(C) Let $z = 1 \pm i \sqrt{3}$. We can write $z$ in polar form as $2(\cos \frac{\pi}{3} \pm i \sin \frac{\pi}{3})$.Then,$(1+i \sqrt{3})^n + (1-i \sqrt{3})^n = [2(\cos \frac{\pi}{3} + i \sin \frac{\pi}{3})]^n + [2(\cos \frac{\pi}{3} - i \sin \frac{\pi}{3})]^n$.Using De Moivre's Theorem,this becomes $2^n(\cos \frac{n \pi}{3} + i \sin \frac{n \pi}{3}) + 2^n(\cos \frac{n \pi}{3} - i \sin \frac{n \pi}{3})$.Simplifying the expression,we get $2^n(2 \cos \frac{n \pi}{3}) = 2^{n+1} \cos \frac{n \pi}{3}$.

If $n$ is a positive integer,then $(1+i \sqrt{3})^n+(1-i \sqrt{3})^n$ is equal to

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