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de Moivre's theorem

\[\ For\ example\ (cos ( \frac{ \pi }{4}\ ) - \ i\sin ( \frac { \pi }{4}\ ))^6 \] \[\ Based\ on\ de\ Moivre's\ theorem,\ we\ must\ rewrite\ (cos θ - \ i\ sin θ)^{n}\ as\ (cos (-θ) + \ i\ sin (-θ) )^{n}\] \[\ Since\ we\ know\ that\ cos (- \pi ) = \cos \pi \ and\ sin (- \pi ) = - \sin \pi \] \[\ Why\ we\ can't\ just\ write\ the\ solution\ as\] \[\ (cos\ 6( \frac{ \pi }{4}\ ) - \ i\sin\ 6( \frac{ \pi }{4}\ ))\ instead\ of \ ( cos\ 6( -\frac{ \pi }{4}\ ) + \ i\sin\ 6( -\frac{ \pi }{4}\ ))\] \[\ After\ all\ at\ the\ end,\ the\ answer\ still\ the\ same. \]

Note by Michael Loh
3 years, 7 months ago

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