Bicomplex number
In abstract algebra, a bicomplex number is a pair (w, z) of complex numbers constructed by the Cayley–Dickson process that defines the bicomplex conjugate ( w , z ) ∗ = ( w , − z ) {\displaystyle (w,z)^{*}=(w,-z)} , and the product of two bicomplex numbers as ( u , v ) ( w , z ) = ( u w − v z , u z + v w ) . {\displaystyle (u,v)(w,z)=(uw-vz,uz+vw).} Then the bicomplex norm is given by ( w , z ) ∗ ( w , z ) = ( w , − z ) ( w , z ) = ( w 2 + z 2 , 0 ) , {\displaystyle (w,z)^{*}(w,z)=(w,-z)(w,z)=(w^{2}+z^{2},0),} a quadratic form in the first component.