I was reading EM Theory from a book when I came across the topic of Wave Impedance. In the book, it says that the wave impedance of a medium is given by the ratio of the magnitudes of E and H of a wave in that medium.
$Z=\frac{|\vec E|}{|\vec H|}$
But, for a conductor we have
$\frac{|\vec H|}{|\vec E|}=\sqrt{\frac{\sigma}{\omega \mu}}$
So, for a good conductor we should have
$|\vec H|>>|\vec E|$
This implies that a conductor should have very low wave impedance.
But, an EM wave is attenuated in a conductor due to the imaginary part of the wave vector. How can both of these be correct?