Precalculus (6th Edition) Blitzer

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

Chapter 6 - Test - Page 800: 11

Answer

The required operation in polar form is $ z=50\left( \cos 20{}^\circ +i\sin 20{}^\circ \right)$

Work Step by Step

Consider the given expression $5\left( \cos 15{}^\circ +i\sin 15{}^\circ \right)\cdot 10\left( \cos 5{}^\circ +i\sin 5{}^\circ \right)$ So, $\begin{align} & 5\left( \cos 15{}^\circ +i\sin 15{}^\circ \right)\cdot 10\left( \cos 5{}^\circ +i\sin 5{}^\circ \right)=\left( 5\cdot 10 \right)\left( \cos \left( 15{}^\circ +5{}^\circ \right)+i\sin \left( 15{}^\circ +5{}^\circ \right) \right) \\ & =50\left( \cos 20{}^\circ +i\sin 20{}^\circ \right) \end{align}$ So, $ z=50\left( \cos 20{}^\circ +i\sin 20{}^\circ \right)$ Therefore, the required operation in polar form is $ z=50\left( \cos 20{}^\circ +i\sin 20{}^\circ \right)$.
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