## Precalculus (6th Edition) Blitzer

Published by Pearson

# 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 $\cos \frac{5\pi }{12}+i\sin \frac{5\pi }{12}$

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