I have the following function of ω

```
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))
```

And I wish to obtain the poles for the denominator of the function:

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

The result is of the following:

```
{-(1/6) I (Γ + κ1 + κ2) + (I (-16 (\
Γ + κ1 + κ2)^2 +
48 (4 g1^2 +
4 g2^2 + Γ κ1 + Γ...}
```

Basically a really long ugly solution. My goal is to obtain the conjugate of wroots1, however, when I do it straightforwardly:

```
wroots2 =
Simplify[Conjugate[wroots1],
Assumptions -> {Γ ∈
Reals, κ1 ∈ Reals, κ2 ∈ Reals,
g1 ∈ Reals,
g2 ∈ Reals, ω ∈ Reals,
4 (-16 (Γ + κ1 + κ2)^2 +
48 (4 g1^2 +
4 g2^2 + Γ κ1 + (Γ + \
κ1) κ2))^3 +
4096 (-36 g1^2 (Γ + κ1 -
2 κ2) + (2 Γ - κ1 - \
κ2) (36 g2^2 + (Γ + κ1 -
2 κ2) (Γ -
2 κ1 + κ2)))^2 > 0}];
```

I am returned with:

```
{1/48 I (8 (Γ + κ1 + κ2) +
8 2^(1/3) (-12 g1^2 -
12 g2^2 + (Γ + κ1 + κ2)^2 -
3 (κ1 κ2 + Γ (κ1 + \
κ2))) Conjugate[
1/(-36 g1^2 Γ + 72 g2^2 Γ +
2 Γ^3 - 36 g1^2 κ1 -
36 g2^2 κ1 - 3 Γ^2 κ1 -
3 Γ κ1^2 + 2 κ1^3 +
72 g1^2 κ2 - 36 g2^2 κ2 -
3 Γ^2 κ2 +
12 Γ κ1 κ2 -
3 κ1^2 κ2 - 3 Γ κ2^2 -
3 κ1 κ2^2 + 2 κ2^3...}
```

Clearly, Conjugate refuses to take the conjugate of said function. I tried doing

```
wroots2 = wroots1 /. {I -> -I}
```

But that doesn’t work as well. I’m at lost at what to do here and I could use any help I can get. Thank you very much in advance.