Find the real part of a given complex number

Let $n \in \mathbb{N}^*$ and $k \in \{0, 1, 2, ..., n - 1\}$.

$$z = \left( \cot \frac{(2k + 1)\pi}{2n} + i \right)^n$$

Find the real part of $z$.

I think we need to transform $z$ into something like $\cos \phi + i \sin \phi$, so we can compute its n-th power using De Moivre's rule. However, I haven't figured out any way to do this yet.

Thank you in advance!