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 767: 39

Answer

The multiplication of the complex numbers in the polar form is $12\left( \cos \frac{3\pi }{10}+i\sin \frac{3\pi }{10} \right)$.

Work Step by Step

Here, $\begin{align} & {{z}_{1}}=3\left( \cos \frac{\pi }{5}+i\sin \frac{\pi }{5} \right) \\ & {{z}_{2}}=4\left( \cos \frac{\pi }{10}+i\sin \frac{\pi }{10} \right) \\ \end{align}$ Therefore, $\begin{align} & {{z}_{1}}\times {{z}_{2}}=3\times 4\left( \cos \left( \frac{\pi }{5}+\frac{\pi }{10} \right)+i\sin \left( \frac{\pi }{5}+\frac{\pi }{10} \right) \right) \\ & =12\left( \cos \frac{3\pi }{10}+i\sin \frac{3\pi }{10} \right) \end{align}$ The multiplication of the complex numbers in the polar form is $12\left( \cos \frac{3\pi }{10}+i\sin \frac{3\pi }{10} \right)$
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