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: 27


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

Work Step by Step

Here $\begin{align} & z=6\left( \cos 30{}^\circ +i\sin 30{}^\circ \right) \\ & =x+iy \end{align}$ Therefore, $x=6\cos 30{}^\circ,y=6\sin 30{}^\circ $ Simplifying it further, to get, $\begin{align} & x=6\times \left( \frac{\sqrt{3}}{2} \right) \\ & =3\sqrt{3} \\ & y=6\times \left( \frac{1}{2} \right) \\ & =3 \end{align}$ So, the rectangular form of the complex number is $3\sqrt{3}+3i$
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