reserve x for Real;

theorem
  for z being Complex holds z = |.z.|*cos Arg z + |.z.|*sin Arg z * <i>
proof
  let z be Complex;
  per cases;
  suppose
    z = 0;
    hence thesis by COMPLEX1:44;
  end;
  suppose
    z <> 0;
    hence thesis by Def1;
  end;
end;
