Oscillations in the cumulative individual income distribution have been found in the data of various countries studied by different authors at different time periods, but the dynamical origins of this behavior are currently unknown. These data sets can be fitted by different functions at different income ranges, but recently the Tsallis distribution has been found capable of fitting the whole distribution by means of only two parameters, procedure which showed even more clearly such oscillatory features in the entire income range. This behavior can be described by assuming log-periodic functions, however a different approach to naturally disclose such oscillatory characteristics is to allow the Tsallis $q$-parameter to become complex. In this paper we have used these ideas in order to describe the behavior of the complementary cumulative distribution function of the personal income of Brazil recently studied empirically by Soares et al. (2016). Typical elements of periodic motion, such as amplitude and angular frequency coupled to this income analysis, were obtained.
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