= Solution
The base is $2e^{i\pi/4}$. Its <complex logarithms> are $\ln2+i(\pi/4+2\pi k)$, $k\in\mathbb Z$. Exponentiating $i$ times each logarithm gives all values of the multivalued power:
$$
\boxed{z_k=e^{-\pi/4-2\pi k}\exp(i\ln2),\qquad k\in\mathbb Z.}
$$
The values form a discrete <geometric sequence> along the Argand ray of angle $\ln2$. Consecutive radii differ by $e^{-2\pi}$. The origin is an accumulation point but is not itself a value. If the power is instead defined using the <principal logarithm>, only $k=0$ is retained. The phrase “all values” requires this branch distinction.
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