## Calculus: Early Transcendentals 8th Edition

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