A1: rng (f ^ g) = (rng f) \/ (rng g) by FINSEQ_1:31;
( rng f c= COMPLEX & rng g c= COMPLEX ) by VALUED_0:def 1;
then rng (f ^ g) c= COMPLEX by A1, XBOOLE_1:8;
hence f ^ g is complex-yielding by VALUED_0:def 1; :: thesis: verum