What I reallyn wnatm though, is
Simplify[Im[ComplexExpand[Exp[I*t]/(q - Exp[I*t])]], Element[{q, t}, Reals]]
which produces
(-1 + q Cos[t]) Im[1/(1 + q^2 - 2 q Cos[t])] + q Re[1/(1 + q^2 - 2 q Cos[t])] Sin[t]
but with real t and q
Im[1/(1 + q^2 - 2 q Cos[t])]
is 0 and
1/(1 + q^2 - 2 q Cos[t])]
is real, therefore Re in the second part of the expression is unneccessary
But what I really need id the following:
Simplify[Im[ComplexExpand[Exp[I*t]/(q - Exp[I*t])]], {Element[{q, t}, Reals], Abs[q] < 1}]
It gives the answer I expect:
(q Sin[t])/(1 + q^2 - 2 q Cos[t])