Frequency-difference electrical impedance tomography (fdEIT) has been proposed to deal with technical difficulties of a conventional static EIT imaging method caused by unknown boundary geometry, uncertainty in electrode positions and other systematic measurement artifacts. In fdEIT, we try to produce images showing changes of a complex conductivity distribution with respect to frequency. Simultaneously injecting currents with at least two frequencies, we find differences of measured boundary voltages between those frequencies. In most previous studies, real parts of frequency-difference voltage data were used to reconstruct conductivity changes and imaginary parts to reconstruct permittivity changes. This conventional approach neglects the interplay of conductivity and permittivity upon measured boundary voltage data. In this paper, we propose an improved fdEIT image reconstruction algorithm that properly handles the interaction. It uses weighted frequency differences of complex voltage data and a complex sensitivity matrix to reconstruct frequency-difference images of complex conductivity distributions. We found that there are two major sources of image contrast in fdEIT. The first is a contrast in complex conductivity values between an anomaly and background. The second is a frequency dependence of a complex conductivity distribution to be imaged. We note that even for the case where conductivity and permittivity do not change with frequency, the fdEIT algorithm may show a contrast in frequency-difference images of complex conductivity distributions. On the other hand, even if conductivity and permittivity values significantly change with frequency, there is an example where we cannot find any contrast. The performance of the proposed method is demonstrated by using computer simulations to validate its feasibility in future experimental studies.