Some authors speak of the ``index of refraction'' and the ``relative permittivity'' (or ``dielectric constant'') as real numbers, as if they do not warrant any discussion of complex numbers. Other authors speak of the ``complex index of refraction'' and the ``complex permittivity.'' But they all seem to agree that the index of refraction squared equals the permittivity. Say the index of refraction is $n'+in''$ and the relative permittivity is $\epsilon'+i\epsilon''$. According to the authors who are only talking about real numbers, I have $n'^2=\epsilon'$. According to those who talk about complex numbers, I have $(n'+in'')^2=\epsilon'+i\epsilon''$. Together, those two equations seem extremely weird, so I can only believe that I am mistaken about something. I think that at least one of the statements I have made so far is incorrect. Can someone please clear up my confusion? Thank you!