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: 28


The rectangular form of the complex number is $6+6\sqrt{3}i$.

Work Step by Step

Here $\begin{align} & z=12\left( \cos 60{}^\circ +i\sin 60{}^\circ \right) \\ & =x+iy \end{align}$ Therefore, $x=12\cos 60{}^\circ,y=12\sin 60{}^\circ $ Simplify it further to get, $\begin{align} & x=12\times \left( \frac{1}{2} \right) \\ & =6 \\ & y=12\times \left( \frac{\sqrt{3}}{2} \right) \\ & =6\sqrt{3} \end{align}$ So, the rectangular form of the complex number is $6+6\sqrt{3}i$
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