reserve a, b, c, d, x, y, z for Complex;

theorem Th28:
  z.|.z = (Re z)*(Re z)+(Im z)*(Im z) & z.|.z = (Re z)^2+(Im z)^2
proof
  thus z.|.z = (Re z)*(Re z)+(Im z)*(Im z)+(-((Im z)*(Re z))+(Im z)*(Re z)
  )*<i> by Th27
    .= (Re z)*(Re z)+(Im z)*(Im z);
  hence thesis;
end;
