Electrical capacitance tomography (ECT) is an imaging method mainly capable of reconstructing dielectric permittivity. Generally, the reactance part of complex admittance is measured in a selected frequency. This paper presents for the first time an in depth and systematic analysis of complex admittance data for simultaneous reconstruction of both electrical conductivity and dielectric permittivity. A complex-valued forward model, Jacobian matrix and inverse solution are developed in the time harmonic excitation mode to allow for multi-frequency measurements. Realistic noise models are used to evaluate the performance of complex admittance ECT in a range of excitation frequencies. This paper demonstrates far greater potential for ECT as a versatile imaging tool through novel analysis of complex admittance imaging using a dual conductivity permittivity inversion method. The paper demonstrates that various classes of contactless capacitance based measurement devices can be analysed through complex multi-frequency ECT.