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QUESTION

Using de Moivre's theorem, or otherwise, calculate
$\ds\left(\cos\left(\frac{\pi}{4}\right)+j\sin\left(\frac{\pi}{4}\right)\right)^4$.




ANSWER

$\ds\left(\cos\left(\frac{\pi}{4}\right)+j\sin\left(\frac{\pi}{4}\right)\right)^4
=\cos(\pi)+j\sin(\pi)=-1+j(0)=-1$




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