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

theorem
  |.z.| ^2 = Rea (z * z*')
proof
  Rea(z*z*') = (Rea z)^2+(Im1 z)^2+(Im2 z)^2+(Im3 z)^2 by QUATERNI:60;
  hence thesis by Th11;
end;
