In this paper we will see that we can avoid the concepts of negative number and complex number thanks to the study of the underlying vector nature of some arithmetic and polynomial problems. We will see that the geometrical models used until now to represent negative numbers and complex numbers and their operations are not just interpretations or models. Translations, rotations and homotheties are what we need to solve several problems. We will see that what we call "negative numbers" and "complex numbers" are just the solutions of vector calculations and equations. All that is the consequence of the fact that geometrical considerations are unavoidable when we think about debts and gains and when we try to solve some polynomial equations. Those considerations are linked to a geometrical system with symmetries and a center. We will see that thanks to the solutions of those vector equations we can construct paths in the plane. We will also give the vector meaning of the formulas of De Moivre and Euler. An interpretation of the vertical axis linked to gains and losses will also be given.