reserve x for Real;

theorem Th3:
  for z be Complex holds |.z.|^2 = (Re z)^2 + (Im z)^2
proof
  let z be Complex;
  thus |.z.|^2 = |.z*z.| by COMPLEX1:65
    .= (Re z)^2 + (Im z)^2 by COMPLEX1:68;
end;
