Show that the real and imaginary parts of the wavenumber, k, are given by

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Homework Statement

Show that the real and imaginary parts of the wavenumber, k, are given by
k(real)=[sqrt(epsilon(real))]omega/c

and k(imaginary)=[epsilon(imaginary) *omega/(2c sqrt(espilon(real)))

The Attempt at a Solution

k^2= mu epsilon omega^2 (1+(i g/epsilon*omega))
k^2 (real)=sqrt (mu epsilon omega^2)
=sqrt(mu epsilon)*omega
=sqrt(mu epsilon(real) epsilon0) omega
=(1/c)sqrt(epsilon(real)) omega

k^imaginary =(mu epsilon omega^2 i g)/(epsilon omega)
=mu omega i g
g is approximately epsilon omega
k^2(imaginary)=mu omega i epsilon omega
k=sqrt(mu epsilon) omega sqrt(i)
=(1/c) omega sqrt(i)
=(1/c) omega (1/(sqrt(2)))(1+i)

 

[member 553083]

=(1/c)(1/(sqrt(2))) epsilon(imaginary) omega+(1/c)(i/(sqrt(2)))(1+i) epsilon(imaginary) omega=(1/c)[epsilon(imaginary) omega/(2 sqrt(epsilon(real)))]