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: 30

Answer

The rectangular form of the complex number is $-5\sqrt{3}-5i$.

Work Step by Step

Here $\begin{align} & z=10\left( \cos 210{}^\circ +i\sin 210{}^\circ \right) \\ & =x+iy \end{align}$ Therefore, $x=10\cos 210{}^\circ,y=5\sin 210{}^\circ $ Simplify it further to get, $\begin{align} & x=10\times (-\frac{\sqrt{3}}{2}) \\ & =-5\sqrt{3} \\ & y=10\times (-\frac{1}{2}) \\ & =-5 \end{align}$ So, the rectangular form of the complex number is $-5\sqrt{3}-5i$
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