In mathematics, the multicomplex number systems are defined inductively as follows: Let C0 be the real number system. For every n > 0 let in be a square root of −1, that is, an imaginary unit. Then . In the multicomplex number systems one also requires that (commutativity). Then is the complex number system, is the bicomplex number system, is the tricomplex number system of Corrado Segre, and is the multicomplex number system of order n.