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