Answer
$e^{\pi}\cos 1+ie^{\pi}\sin 1$
Work Step by Step
We use Equation 7 from the text (a modification of Euler's formula), $e^{x+iy}=e^x(\cos{y}+i\sin{y})$:
$e^{\pi+i}=e^{\pi+1*i}=e^{\pi}(\cos 1+i\sin 1)=e^{\pi}\cos 1+ie^{\pi}\sin 1$
Calculus 8th Edition
by Stewart, James
Published by
Cengage
ISBN 10:
1285740629
ISBN 13:
978-1-28574-062-1
Appendix G - Complex Numbers - G Exercises - Page A56: 46
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