Unitarity and Analyticity of scattering amplitudes, when combined with Cauchy's Residue Theorem and its multivariate generalizations via Stokes' Theorem, turn into powerful techniques for evaluating radiative corrections. In the context of the by-now known as unitarity-based methods, I shall review how the simple implementation of complex momenta for propagating particles enable us to carry out the calculation of tree-level and one-loop amplitudes very efficiently, and to provide, as well, the Optical Theorem with a geometrical interpretation as a Berry's phase.