I can get a rough approximation using geometer's sketchpad and moving points a and b around a bit. (c and d are reflections over the real axis = easier and imaginary parts always cancel)

a = .76 + .35i b = -.26 + .71i

The equations come out to

1 .04 1.05 -.06

I think the solution is in the vicinity of this but moving one pixel changes the numbers rather unpredictably.