# Unable to solve for roots (trivial) [closed]

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.

• Iω is different from I ω; mind your spaces when multiplying variables! – J. M. will be back soon Mar 16 '18 at 18:32
• I've fixed it as 'I*[Omega]' but it still doesn't work. – kowalski Mar 16 '18 at 18:37
• 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]]. – george2079 Mar 16 '18 at 21:55

Iw is a variable name; I w is Sqrt[-1] w. Therefore,
f[ω_] :=