reserve a,b,c,d for Real;
reserve z,z1,z2 for Complex;

theorem
  Re(z*z) = (Re z)^2 - (Im z)^2 & Im(z*z) = 2*(Re z *Im z)
proof
  thus Re(z*z) = (Re z)^2 - (Im z)^2 by Th9;
  thus Im(z*z) = Re z *Im z + Re z *Im z by Th9
    .= 2*(Re z *Im z);
end;
