counter example y + f ( 2 ) = i 2 2 if ( x , y ) = C / { (0,0) } r ty if (x, y) = (0,0) Claim 1 f cont at (0,0) Claim 2 f is not diff at (0,0) HW2 f , f, are not continuous at (0,0) HW3 H(C ) = {f : C-C diff on C} Find { fE H(C ) : f + fe H(C ) ) and { fe H(C ) : f - fe H(C) } f := utiv , f := u- iv