Calculus 8th Edition

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

Appendix G - Complex Numbers - G Exercises: 45

Answer

$-e^{2}$

Work Step by Step

We use Equation 7 from the text (a modification of Euler's formula), $e^{x+iy}=e^x(\cos{y}+i\sin{y})$: $e^{2+i\pi}=e^{2}(\cos\pi+i\sin\pi)=e^{2}(-1+i*0)=e^2(-1)=-e^{2}$
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