Real component of the wavelength of microwaves in copper

[buttons123]

I am trying to work out the real component of the wavelength of microwaves in copper. I am given n²=e_r=-i sigma/e_o omega

where n is the refactive index
e_r is the relative permitivity
e_o is the permitivity of free space
i = sqrt(-1)
omega is the frequency of the microwave
sigma is the conductivity of copper

I was approaching this by using n=kc/omega where k is the wavenumber and then c=f*wavelength but I am not sure about obtaining the real part of the refractive index as the whole value is multiplied by i?

Any ideas or examples/links would be helpful.

 

[Born2bwire]

For microwaves it really doesn't matter as the imaginary part is much much larger than the real part. The real part does become more significant as we go above microwaves and approach the plasma resonance of the metal. If you really want to find the real part, I would suggest finding the Drude model for copper that simulates it as having a plasma resonance. I do not know off hand what the constants are for copper in the model.