We apply a constant voltage between a distal reference electrode and a scan probe placed on the surface of a region of interest. The probe includes an array of electrodes kept at the ground potential and exit currents from those electrodes are measured. Using multiple sinusoidal frequencies in the range of 50Hz to 500kHz, the relationship between a frequency-difference trans-admittance map and a complex conductivity distribution underneath the probe can be expressed by a pair of partial differential equations coupled through conductivity and permittivity distributions. With possible applications of breast cancer detection in mind, we constructed a three-dimensional model of the breast containing an anomaly with complex conductivity different from those of its surrounding inhomogeneous background tissues. From a mathematical analysis of this multi-frequency TAS model, we found that the imaginary part of a weighted frequency-difference trans-admittance map contains the size and location information of the anomaly. We demonstrate the feasibility of the method using numerical simulations.