extracting the time averaged magnitude of the poynting vector

I have a question about how to extract the time averaged magnitude of the poynting vector at a particular voxel from my simulations.
I ran a harmonic simulation of a dipole model, with an overall field sensor. When the simulation ended, I exported the S(x,y,z,f0) variable of the overall field sensor to matlab. Then, when I open the snapshot variable in matlab, I see three columns with numbers having a real and an imaginary part. I assume that each column corresponds to the x,y,z complex values of the poynting vector at each voxel. Then, my question is, in order to calculate the time averaged magnitude of the poynting vector at each voxel, should I just compute ½ times the real part of the complex values in this snapshot variable? Or should I compute the magnitude of these complex values by computing the square root of: real part squared + imaginary part squared?


In Sim4Life, the complex field S(x,y,z,f0) is (one half of) the cross product of the complex fields E(x,y,z,f0) and H(x,y,z,f0), both of which are the complex representation of harmonic fields (actually S = 0.5 E cross H*, where H* is the complex conjugate of H)
The time-averaged Poynting vector (if you want the power flow) is given by Re(S)

See the Wikipedia article (https://en.wikipedia.org/wiki/Poynting_vector) for more detail.

EDIT: this post was corrected to reflect the notations used in Sim4Life, namley that S(x,y,z,f0) is already the time-averaged quantity and includes the factor 1/2.