Q:

Unable to solve for roots (trivial)

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.

A:

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:

