Rotation of the SED in the complex plane for a sum of seven MBB SEDs with distinct spectral indices drawn from a Gaussian distribution with mean 1.5 and standard deviation 0.1 (red), or with temperatures drawn from a Gaussian distribution with mean 20 K and standard deviation 5 K (blue). The 3D orientation of the magnetic field is a random realization of the turbulent magnetic field inspired by Planck Collaboration Int. XLVIII (2016). The dashed lines indicate frequencies from 40 to 400 GHz, and the four colored points represent the Planck HFI bands.