Its wave vector Kz is equal to:
Then, I read also that it is true that:
where does this relation come from?
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The wavenumber \$k\$ is the result of solving the differential equations of the (general) electromagnetic wave for \$E\$ and \$H\$ in e.g. free space. The result for \$k\$ consists of the material characteristics \$\mu,\epsilon,\sigma\$.
When solving the telegrapher equations for the coaxial cable, you also get \$k\$, but this time \$k\$ consists of an R,L,G & C expression.
So the wavenumber \$k\$ comes either from the definition of a general wave or from the definition of a generic transmission line like e.g. a coaxial cable.
(The phase constant \$\beta\$ is just the imaginary component of \$k\$.)