 The identity component is parameterized by ρ and exp("a m") = cosh("a") + "m" sinh("a").Now formula_9 regardless of the subplane P"m", but the argument of the function must be taken from the "identity component of its group of units".Half the plane is lost in the case of the dual number structure; three-quarters of the plane must be excluded in the case of the split-complex number structure.