Answer
$\frac{1}{2}+\frac{\sqrt{3}}{2}i$
Work Step by Step
Given: $e^{i\pi/3}$
To write the number as $a+bi$, we apply Euler's formula, $e^{iy}=\cos{y}+i\sin{y}$
$e^{i\pi/3}=\displaystyle \cos\frac{\pi}{3}+i\sin\frac{\pi}{3}$
$=\frac{1}{2}+i\frac{\sqrt{3}}{2}$
$=\frac{1}{2}+\frac{\sqrt{3}}{2}i$
