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Having a big issue working through this problem and was wondering if somebody, much smarter than I, could give me a few pointers. Anyway here's the problem:

Given that k

By writing the wave number as k=k

Show that k

k

I've started by equating real and imaginary parts however I find an impasse where I have a quartic equation.

I'd been incredibly grateful for any answers, thank you in advance!

Just as a quick note, I followed the following process but reached an impasse (may be completely off base here):

k

Substitute k=k

k

Then split into two equations by equating real and imaginary parts;

(1) k

(2) εμω

Now (2) into (1) gives;

(ωμσ/2k

Then rearranging gives;

k

[EDIT: Realised i'd been a bit of an idiot and missed what should have been quite obvious, thank you for pointing it out!]

Given that k

^{2}=εμω^{2}-iωμσBy writing the wave number as k=k

_{r}-ik_{i}.Show that k

_{i}, which determines attenuation, can be expressed by:k

_{i}=ω(εμ/2)^{1/2}[(1+(σ^{2}/ω^{2}ε^{2}))^{1/2})-1]^{1/2}I've started by equating real and imaginary parts however I find an impasse where I have a quartic equation.

I'd been incredibly grateful for any answers, thank you in advance!

Just as a quick note, I followed the following process but reached an impasse (may be completely off base here):

k

^{2}=εμω^{2}-iωμσSubstitute k=k

_{r}-ik_{i}. into the equation which gives;k

_{r}^{2}-2ik_{r}k_{i}-k_{i}^{2}=εμω^{2}-iωμσThen split into two equations by equating real and imaginary parts;

(1) k

_{r}^{2}-k_{i}^{2}=εμω^{2}(2) εμω

^{2}=ωμσ/2k_{i}Now (2) into (1) gives;

(ωμσ/2k

_{i})^{2}-k_{i}^{2}=εμω^{2}Then rearranging gives;

k

_{i}^{4}+εμω^{2}k_{i}^{2}=ω^{2}μ^{2}σ^{2}/4[EDIT: Realised i'd been a bit of an idiot and missed what should have been quite obvious, thank you for pointing it out!]

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