Precalculus (6th Edition) Blitzer

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

Chapter 6 - Section 6.7 - The Dot Product - Exercise Set - Page 799: 66


$\cos 265{}^\circ +i\sin 265{}^\circ $

Work Step by Step

Product of two complex numbers: The product of two complex numbers ${{z}_{1}}={{r}_{1}}\left( \cos {{\theta }_{1}}+i\sin {{\theta }_{1}} \right)$ and ${{z}_{2}}={{r}_{2}}\left( \cos {{\theta }_{2}}+i\sin {{\theta }_{2}} \right)$, is given by ${{z}_{1}}\cdot {{z}_{2}}={{r}_{1}}\cdot {{r}_{2}}\left[ \cos \left( {{\theta }_{1}}+{{\theta }_{2}} \right)+i\sin \left( {{\theta }_{1}}+{{\theta }_{2}} \right) \right]$ So, the product of the given complex numbers ${{z}_{1}}=\left( \cos 210{}^\circ +i\sin 210{}^\circ \right)\text{ and }{{z}_{2}}=\left( \cos 55{}^\circ +i\sin 55{}^\circ \right)$ is as follows: $\begin{align} & {{z}_{1}}\cdot {{z}_{2}}=1\cdot 1\left[ \cos \left( 210+55 \right)+i\sin \left( 210+55 \right) \right] \\ & =\cos 265{}^\circ +i\sin 265{}^\circ \end{align}$ Hence, the product of the complex numbers is $\cos 265{}^\circ +i\sin 265{}^\circ $.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.