  We study the Delta^{++} contributions to elastic and radiative \pi^+p
scattering within an effective Lagrangian model which incorporates the Delta,
N, rho and sigma meson degrees of freedom. This model provides a description of
the Delta resonance and its interactions that respects electromagnetic gauge
invariance and invariance under contact transformations when finite width
effects are incorporated. Following recent developments in the description of
unstable gauge bosons, we use a complex mass scheme to introduce the finite
width of the Delta^{++} without spoiling gauge invariance. The total cross
section of elastic \pi^+p scattering, whose amplitude exhibits the resonant
plus background structure of S-matrix theory, is used to fix the mass, width
and strong coupling of the \Delta resonance. The differential cross section of
elastic scattering is found in very good agreement with experimental data. The
magnetic dipole moment of the Delta^{++}, \mu_{Delta}, is left as the only
adjustable parameter in radiative \pi^+p scattering. From a fit to the most
sensitive configurations for photon emission in this process, we obtain
\mu_{\Delta} = (6.14 +-0.51)e/2m_p, in agreement with predictions based on the
SU(6) quark model.
