Answer
$e^{\pi}\cos 1+ie^{\pi}\sin 1$
Work Step by Step
Use Euler's formula, $e^{x+iy}=e^x(\cos{y}+i\sin{y})$:
$e^{\pi+i}=e^{\pi+1*i}=e^{\pi}(\cos 1+i\sin 1)$
$=e^{\pi}\cos 1+ie^{\pi}\sin 1$
Multivariable Calculus, 7th Edition
by Stewart, James
Published by
Brooks Cole
ISBN 10:
0-53849-787-4
ISBN 13:
978-0-53849-787-9
Appendix G - Exercises - Page A12: 46
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