<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\documentclass[a4paper,12pt]{article}
\newcommand\ds{\displaystyle}
\begin{document}

\parindent=0pt

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

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




\end{document}
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