Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Appendix G - Complex Numbers - G Exercises - Page A56: 46


$e^{\pi}\cos 1+ie^{\pi}\sin 1$

Work Step by Step

We use Equation 7 from the text (a modification of Euler's formula), $e^{x+iy}=e^x(\cos{y}+i\sin{y})$: $e^{\pi+i}=e^{\pi+1*i}=e^{\pi}(\cos 1+i\sin 1)=e^{\pi}\cos 1+ie^{\pi}\sin 1$
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