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Let \(z = 3[\cos(85^{\circ})+i\sin(85^{\circ})]\). Find the smallest positive value of \(r\) such that \(r[\cos(45^{\circ})+i\sin(45^{\circ})] = z^n\) for some positive integer \(n\).

 Dec 20, 2019
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By DeMoivre's Theorem, the smallest possible value of r is 3^6 = 729.

 Dec 20, 2019

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