reserve z1,z2,z3,z4,z for Quaternion;

theorem Th24:
  Rea (1/(|.z.| ^2) * z*') = 1/(|.z.| ^2)*Rea z
proof
  z*' = [*Rea z, -Im1 z, -Im2 z, -Im3 z*] by QUATERNI:43; then
  (1/(|.z.| ^2) * z*') = [*1/(|.z.| ^2)*Rea z, 1/(|.z.| ^2)*(-Im1 z), 1/(
  |.z.| ^2)*(-Im2 z), 1/(|.z.| ^2)*(-Im3 z)*] by QUATERNI:def 21;
  hence thesis by QUATERNI:23;
end;
