Surcomplex number

A surcomplex number is a number of the form $a+bsqrt\{-1\}$, where "a" and "b" are surreal numbers. [ [http://jamespropp.org/surreal/text.ps.gz Surreal vectors and the game of Cutblock] , James Propp, August 22, 1994.] [N. L. Alling, "Foundations of analysis over surreal number fields", N. L. Alling, Amsterdam: North-Holland, 1987. ISBN 0-444-70226-1.] The surcomplex numbers form an algebraically closed field, isomorphic to the algebraic closure of the rational numbers extended by a proper class of algebraically independent transcendental elements. Up to field isomorphism, this fact characterizes the field of surcomplex numbers. [Theorem 27, "On Numbers and Games", John H. Conway, 2nd ed., Natick, Massachusetts: A K Peters, Ltd., 2000. ISBN 1-56881-127-6.]

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