I have been told in the university that the natural frequencies (also called $\textit{eigenfrequencies}$) are the poles of the transfer function, however, Matlab compute them as the modulus of the pole (information taken from here).
So the real question is, are the natural frequencies complex numbers or real numbers measured in rad/s?
The natural frequency is a real number, and Matlab computes it correctly by taking the magnitude of the (complex-valued) pole.
As an example, the denominator of the transfer function of a second-order continuous-time system is given by
$$D(s)=s^2+2\omega_n\zeta s+\omega_n^2\tag{1}$$
where $\zeta$ is the damping ratio, and $\omega_n$ is the natural frequency. The poles are given by the roots of $(1)$. Assuming an underdamped system ($\zeta<1)$, the poles are given by
$$s_{\infty}=-\omega_n\left(\zeta\pm j\sqrt{1-\zeta^2}\right)\tag{2}$$
from which we get
$$|s_{\infty}|^2=\omega_n^2\left[\zeta^2+(1-\zeta^2)\right]=\omega_n^2\tag{3}$$
So the natural frequency $\omega_n$ is given by the magnitude of the pole $s_{\infty}$.
Note that the natural frequency $\omega_n$ is not the actual oscillation frequency unless there is no damping (i.e., $\zeta=0$).
