THINK ABOUT IT THIS WAY:
a + jb = A at angle θ, where θ = arctan(b/a)
1/(a + jb) = (1/A) at angle -θ.
Multiplying complex numbers adds the angles, dividing complex numbers subtracts the angle of the divisor from the angle of the dividend.
fantaci, is correct however, that complex poles ALWAYS APPEAR IN CONJUGATE PAIRS, so your equation (2) never happens in real systems. You can for academic interests find the angle of H. You can rewrite (2) as:
H = A(a+jb)/(a+j(w+b))
the angle of H = angle of (a+jb) minus the angle of (a + j(w+b)).