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

theorem
  |.z*z.| = (Re z)^2 + (Im z)^2
proof
  0<=(Re z)^2 + (Im z)^2 & |.z*z.| = |.z.|*|.z.| by Lm1,Th65;
  then |.z*z.| = sqrt (((Re z)^2 + (Im z)^2)^2) by SQUARE_1:29;
  hence thesis by Lm1,SQUARE_1:22;
end;
