Example 7. Calculate $(-1+i \sqrt{3})^{60}$.

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Solution. Let's represent the number $z=-1+i \sqrt{3}$ in trigonometric form

$$
-1+i \sqrt{3}=2\left(\cos \frac{2}{3} \pi+i \sin \frac{2}{3} \pi\right)
$$

Applying the above formula for raising to a power, we get

$$
\begin{aligned}
(-1+i \sqrt{3})^{60} & =2^{60}\left[\cos \left(60 \cdot \frac{2}{3} \pi\right)+i \sin \left(60 \cdot \frac{2}{3} \pi\right)\right]= \\
& =2^{60}(\cos 40 \pi+i \sin 40 \pi)=2^{60}
\end{aligned}
$$