Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 6 - Section 6.5 - Complex Numbers in Polar Form; DeMoivre's Theorem - Exercise Set - Page 768: 57


The power of the complex numbers in the rectangular form is $\frac{i}{64}$.

Work Step by Step

Here, $z={{\left[ \frac{1}{2}\left( \cos \frac{\pi }{12}+i\sin \frac{\pi }{12} \right) \right]}^{6}}$ (I) Therefore $\begin{align} & z={{\left[ \frac{1}{2}\left( \cos \frac{\pi }{12}+i\sin \frac{\pi }{12} \right) \right]}^{6}} \\ & z=\frac{1}{{{2}^{6}}}\left( \cos 6\times \frac{\pi }{12}+i\sin 6\times \frac{\pi }{12} \right) \\ & z=\frac{1}{64}\left( \cos \frac{\pi }{2}+i\sin \frac{\pi }{2} \right) \\ & z=\frac{1}{64}\left( 0+i \right) \\ \end{align}$ Simplify it further, to get, $z=\frac{i}{64}$ The complex number in the rectangular form is $z=\frac{i}{64}$
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