Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

APPENDIX H - Complex Numbers - H Exercises: 43

Answer

$\frac{1}{2}+\frac{\sqrt{3}}{2}i$

Work Step by Step

To write the number as $a+bi$, we apply Euler's formula, $e^{iy}=\cos{y}+i\sin{y}$ $e^{i\pi/3}=\displaystyle \cos\frac{\pi}{3}+i\sin\frac{\pi}{3}=\frac{1}{2}+i\frac{\sqrt{3}}{2}=\frac{1}{2}+\frac{\sqrt{3}}{2}i$
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