For the vector $psi = { 0,F1,alpha ,0,beta ,0,0,F2} $, I am trying to simplify ${left| psi right|^2}$ where

$alpha = cos (theta )$,

$beta = sin left( theta right)$,

$F1 = {{cos left( theta right)nu } over {{{left( {1 – {{rm{e}}^{ – {{2pi Omega } over r}}}} right)}^{1/2}}}}$, and

$F2 = {{sin left( theta right)nu {{rm{e}}^{ – {{pi Omega } over r}}}} over {{{left( {1 – {{rm{e}}^{ – {{2pi Omega } over r}}}} right)}^{1/2}}}}$, and all parameters ($theta, nu,Omega,r $) are reals. I used:

```
(Alpha) = Cos((Theta));
(Beta) = Sin((Theta));
F1 = (Cos((Theta)) (Nu))/(1 - E^(-((2 (Pi) (CapitalOmega))/r)))^(
1/2);
F2 = ( Sin((Theta)) (Nu) E^(-(((Pi) (CapitalOmega))/r)))/(1 -
E^(-((2 (Pi) (CapitalOmega))/r)))^(1/2);
(Psi) = {0, F1, (Alpha), 0, (Beta), 0, 0, F2};
FullSimplify(
Norm((Psi))^2, {(CapitalOmega), (Nu), r, (Theta)} (Element)
Reals)
```

But Mathematica still considers $r$ is complex, where the output contains the term ${mathop{rm Re}nolimits} left( {{1 over r}} right)$.

Did I miss anything?