Solution
= Solution
The logarithms of $1+\omega=e^{i\pi/3}$ are
$$
i\left(\frac\pi3+2\pi k\right),\qquad k\in\mathbb Z.
$$
The definition of <complex exponentiation> therefore gives all values as
$$
\exp\!\left[
i(1+\omega)\left(\frac\pi3+2\pi k\right)
\right].
$$
Since $1+\omega=\tfrac12+i\tfrac{\sqrt3}{2}$, these can be written
$$
\boxed{
(-1)^k e^{-\sqrt3\pi(k+1/6)}e^{i\pi/6}},
\qquad k\in\mathbb Z.
$$