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: 42

Answer

The multiplication of the complex numbers in the polar form is $\cos \frac{5\pi }{12}+i\sin \frac{5\pi }{12}$.

Work Step by Step

Here, $\begin{align} & {{z}_{1}}=1\left( \cos \frac{\pi }{6}+i\sin \frac{\pi }{6} \right) \\ & {{z}_{2}}=1\left( \cos \frac{\pi }{4}+i\sin \frac{\pi }{4} \right) \\ \end{align}$ Therefore $\begin{align} & {{z}_{1}}\times {{z}_{2}}=1\times 1\left( \cos \left( \frac{\pi }{4}+\frac{\pi }{6} \right)+i\sin \left( \frac{\pi }{4}+\frac{\pi }{6} \right) \right) \\ & =\cos \frac{5\pi }{12}+i\sin \frac{5\pi }{12} \end{align}$ The multiplication of the complex numbers in the polar form is $\cos \frac{5\pi }{12}+i\sin \frac{5\pi }{12}$
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.