  Oscillations in the complementary cumulative distribution function (CCDF) of
individual income data 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. Although these datasets can be fitted by
different functions at different income ranges, the Tsallis distribution has
recently been found capable of fitting the whole distribution by means of only
two parameters. This procedure showed clearly such oscillatory feature in the
entire income range feature, but made it particularly visible at the tail of
the distribution. Although log-periodic functions fitted to the data are
capable of describing this behavior, a different approach to naturally disclose
such oscillatory characteristics is to allow the Tsallis $q$-parameter to
become complex. In this paper we use this idea in order to describe the
behavior of the CCDF of the Brazilian personal income 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 by means of this approach. A highly non-linear function for the CCDF
was obtained through this methodology and a numerical test showed it capable of
recovering the main oscillatory feature of the original CCDF of the personal
income data of Brazil.
