Hi, I'm hoping someone out there is going to see something in this problem that I don't because I really don't get it:(adsbygoogle = window.adsbygoogle || []).push({});

Consider the equation:

[tex]

\sigma=(\omega + i \nu k^2)+\frac{\alpha^2}{\omega + i \eta k^2}

[/tex]

It doesn't really matter what the variables mean, (i^2=-1 of course) but what I really need is to figure out [tex] \omega [/tex], which is complex, as a function of the rest (under a certain approximation). The book I found this in claims that under the following conditions:

[tex]

|\sigma|>>|\alpha|

[/tex]

as well as some vague statement about [tex] \nu, \eta [/tex] being small, the two roots of the quadratic are:

[tex]

\omega \approx -i \nu k^2 + \sigma + \frac{\alpha^2}{\sigma + i(\eta-\nu)k^2}

[/tex]

and

[tex]

\omega \approx -i \eta k^2 - \frac{\alpha^2}{\sigma}

[/tex]

I don't know how they came up with this, but it would be really great to find out. Anybody have any ideas?

Thanks,

dhris

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# Quadratic Problem

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