Exercise 63.23.2. Let $\alpha _1, \ldots , \alpha _ n \in \mathbf{C}$. Then for any conic sector containing the positive real axis of the form $C_\varepsilon = \{ z \in \mathbf{C} \ | \ |\arg z| < \varepsilon \}$ with $\varepsilon > 0$, there exists an integer $k \geq 1$ such that $\alpha _1^ k, \ldots , \alpha _ n^ k \in C_\varepsilon$.

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