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Find an expression for the attenuation from the eqn given

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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 k2=εμω2-iωμσ

By writing the wave number as k=kr-iki.
Show that ki, which determines attenuation, can be expressed by:
ki=ω(εμ/2)1/2[(1+(σ22ε2))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):
k2=εμω2-iωμσ
Substitute k=kr-iki. into the equation which gives;
kr2-2ikrki-ki2=εμω2-iωμσ
Then split into two equations by equating real and imaginary parts;
(1) kr2-ki2=εμω2
(2) εμω2=ωμσ/2ki
Now (2) into (1) gives;
(ωμσ/2ki)2-ki2=εμω2
Then rearranging gives;
ki4+εμω2ki22μ2σ2/4

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

Dr Transport

Science Advisor
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it is a quadratic... set [itex] k_{i} = \alpha [/itex] and us the quadratic equation for [itex] \alpha [/itex] and take the square root.....
 
Actually really disappointed i myself for not seeing that.... Thank you for that, really made this a lot easier.
 

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