Spontaneous self-excitation in induction generators is a fascinating phenomenon triggered by the instability of a zero equilibrium state. Prediction of this condition for various values of free parameters requires many computations of the eigenvalues of a 6 X 6 matrix over a large space. The technical note uses a novel approach to stability using a transformation of the state-space system and an extension of the Hurwitz test to polynomials with complex coefficients. The analytic formulas that are obtained give the values of the minimum load resistance, the range of capacitor values, and the range of speeds for which spontaneous self-excitation appears. The technical note concludes with an illustration of the results on an example.