We use magnetic long-range order as a tool to probe the Cooper-pair wave function in the iron arsenide superconductors. We show theoretically that antiferromagnetism and superconductivity can coexist in these materials only if Cooper pairs form an unconventional, sign-changing state. The observation of coexistence in Ba(Fe1−xCox)2As2 then demonstrates unconventional pairing in this material. The detailed agreement between theory and neutron-diffraction experiments, in particular, for the unusual behavior of the magnetic order below Tc, demonstrates the robustness of our conclusions. Our findings strongly suggest that superconductivity is unconventional in all members of the iron arsenide family.