The measurement of acoustic intensity normally assumes that the intensity is a real quantity; however, it has been shown that intensity may also be viewed as a complex quantity in which the real (active) part is related to the magnitude of the local mean energy flow, and the imaginary (reactive) part is related to the local oscillatory transport of energy. The complex intensity field scattered by an obstruction in a circular duct is investigated here. The intensity field is assumed to be generated by a monopole source and sound is scattered by a symmetrical obstruction placed downstream of the source. The complex intensity field predictions are generated using an analytic mode matching scheme. After decomposing intensity into its active and reactive components, predictions are compared for two different obstructions at a fixed frequency. Conclusions are then drawn on the suitability of using complex intensity to recover information about obstructions in ducts.