Combining the phase of two waves with different polarizations

For any antenna, we have two components of the electric field in the far field region Eθ and EΦ. Both components are complex: they have magnitude and phase. We can get the magnitude of the total electric field using Pythagoras. My question is: how can we get the phase of the total electric field?

In HFSS for example, I can design any antenna and view the magnitude and phase of Eθ and EΦ and I can plot the magnitude of Etotal (the resultant) but the phase information is not there. Can we compute it?