Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.2 Trigonometric (Polar) Form of Complex Numbers - 8.2 Exercises: 36

Answer

The rectangular form is $\frac{\sqrt{6}}{2}$ $- \frac{\sqrt{6}}{2} i$

Work Step by Step

$\sqrt{3}$ $cis$ $315^\circ$ = $\sqrt{3}$ $(cos 315^\circ$ + $isin 315^\circ)$ = $\sqrt{3} \cdot \frac{\sqrt{2}}{2}$ + $\sqrt{3} \cdot i \cdot (- \frac{\sqrt{2}}{2})$ = $\frac{\sqrt{6}}{2}$ $- \frac{\sqrt{6}}{2} i$ The rectangular form is $\frac{\sqrt{6}}{2}$ $- \frac{\sqrt{6}}{2} i$
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