Hi Henrick,
g1 = Graph[{2 \[DirectedEdge] 1, 3 \[DirectedEdge] 2,
4 \[DirectedEdge] 3, 4 \[DirectedEdge] 1},
EdgeWeight -> {2 \[DirectedEdge] 1 -> 2 + 5 I,
3 \[DirectedEdge] 2 -> 4 - 6 I, 4 \[DirectedEdge] 3 -> 1 + 8 I,
4 \[DirectedEdge] 1 -> 7 - 7 I}
];
Graph[g1,
EdgeStyle -> {e_ :> Directive[Thick, If[Im@PropertyValue[{g1, e}, EdgeWeight] < 0, Red, Green]]},
EdgeLabels -> "EdgeWeight"]