Analytical Formula for the Roots of the General Complex Cubic Polynomial

We present a new method to calculate analytically the roots of the general complex polynomial of degree three. This method is based on the approach of appropriate changes of variable involving an arbitrary parameter. The advantage of this method is to calculate the roots of the cubic polynomial as closed formula using the standard convention of the square and cubic roots. In contrast, the reference methods for this problem, as Cardan–Tartaglia and Lagrange, give the roots of the cubic polynomial as expressions with case distinctions which require a convention of roots depending on coefficients.