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In this letter, the resonant frequencies associated with dielectric bodies is investigated in the frequency domain. The Cauchy method is applied directly in the frequency domain to extract the singularity expansion method (SEM) poles of dielectric spheres having different parameters such as permittivity and conductivity, in contrast to the latter method where it is carried out in the time domain. Simulation examples are analyzed to illustrate the potential of this methodology. It is seen that the value of the dielectric constant has little effect on the resonant frequency of a dielectric sphere. This is rather surprising and is in contrast to the resonant frequencies of a conducting sphere, which vary appropriately with the size of the structure.