0
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I have the following function:

f[ω_] := (2 Sqrt[Γ] (4 g2^2 + (κ1 - 
   2 Iω) (κ2 - 2 Iω)))/(
4 g2^2 (Γ - 
 2 Iω) + (4 g1^2 + (Γ - 
    2 Iω) (κ1 - 2 Iω)) (κ2 - 
 2 Iω))

And I wish to solve for the roots of its denominator. I do the following:

wroots1 = Solve[Denominator[f] == 0, ω] // FullSimplify

However, that spits out just

{}

I suspect it's the naming of the variable ω, so I redefined the variable like so:

wroots1 = x /. Solve[(Denominator[f] /. {ω -> x}) == 0, x]//FullSimplify

and I get only

x

I know this might be a trivial issue but I've spent an hour on this. Thank you very much in advance.

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  • 1
    $\begingroup$ is different from I ω; mind your spaces when multiplying variables! $\endgroup$ – J. M.'s discontentment Mar 16 '18 at 18:32
  • $\begingroup$ I've fixed it as 'I*[Omega]' but it still doesn't work. $\endgroup$ – kowalski Mar 16 '18 at 18:37
  • 2
    $\begingroup$ you made the exact same mistake here as in this question mathematica.stackexchange.com/q/167673/2079. You define a function f[w_] := ... In order to use such function as you are trying to do you need to supply arguments when you evaluate. Denominator[f[w]]. $\endgroup$ – george2079 Mar 16 '18 at 21:55
1
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Iw is a variable name; I w is Sqrt[-1] w. Therefore,

f[ω_] := 
  (2 Sqrt[Γ] (4 g2^2 + (κ1 - 2 I ω) (κ2 - 2 I ω))) / 
    (4 g2^2 (Γ - 2 I ω) + (4 g1^2 + (Γ - 2 I ω) (κ1 - 2 I ω)) (κ2 - 2 I ω))
Solve[Denominator[f[ω]] == 0, ω] // Short

This gives a big result:

result

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