I think what you have found is an explicit symbolic output. Perhaps what you want is an expression that does not involve Im
and I
? For that kind of purposes you can use ComplexExpand
. However, in your special case you have square roots that make things complicated, as ComplexExpand
works in the geneal case of a complex-valued square root. In the assumption that those square roots have real values (that may or may not be your situation), you can bypass the roots with a trick and get a formula that is not too complicated:
sost1 = {Sqrt[(2 + (-1 + g) m1^2)/(1 - g + 2 g m1^2)] -> root1,
1/Sqrt[((2 + (-1 + g) m1^2)/(1 - g + 2 g m1^2))] -> 1/root1,
Sqrt[1 - z^2] -> root2};
sost2 = {root1 -> Sqrt[(2 + (-1 + g) m1^2)/(1 - g + 2 g m1^2)],
root2 -> Sqrt[1 - z^2]};
Simplify[ComplexExpand[Im[prigid0[-I z]] /.
sost1]] /. sost2