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

theorem Th27:
  Im3 (1/(|.z.| ^2) * z*') = -1/(|.z.|^2)*Im3 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;
