looks like, with good old derive, it takes seconds to solve this...
please give me a reply, so i've sth about maple to believe in :)

Dear Robert, thanks a lot for your reply. though, i wasn't able to post again yet.

so, i've got some new commands, which don't solve the problem. i paste the the original code, "simplified". lots of variables - without them, it's possible to solve. if they're used as values, no way!

> restart:
> with(linalg):
>
> omega[1][6] := 7.077500000:
> omega[2][6] := 26.10450000:
> omega[3][6] := 54.41300000:
> omega[4][6] := 88.04050000:
>                      
> eta[1][6] := .5785000000e-1:
> eta[2][6] := .7735000000e-2:
> eta[3][6] := .8760000000e-2:
> eta[4][6] := .3143500000e-1:
>
> r[1][2] := .152-.58e-1*I:
> r[2][2] := .262-.80e-1*I:
> r[3][2] := .235-.10e-1*I: 
> r[4][2] := .426-.755*I:
>
> alpha[1,1] := sum((r[n][2]/(omega[n][6]^2 - omega^2 + I * eta[n][6] * omega[n][6]^2)),n=1..4);
> a1 := map(evalc @ Re, alpha[1,1]);
> a2 := map(evalc @ Im, alpha[1,1]);
 

so hopefully somebody can give me a hint, thx a lot for them.

max!