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 768: 87

Answer

Please see below.

Work Step by Step

By using the identity $e^{i \theta }= \cos \theta + i \sin \theta$, we have$$e^{\frac{\pi i}{4}}=\cos \frac{\pi }{4} + i \sin \frac{\pi }{4}=\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i.$$Now, we plot the complex number $z=\frac{\sqrt{2}}{2}+ \frac{\sqrt{2}}{2}i$ the same way we plot $(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$ in the rectangular coordinate system.
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