. Suppose that F(x, y) = (Fi(x, y) , F2(x, y) ) is a twice continuously differentiable vector field with the property that OF1 OF2 OF1 OF2 (* ) and ax ay ay Show that both F1 and F2 are harmonic, i.e., AF1 = 0= AF2, where A = 82 daz + dy . Let F(x, y) be a continuously differentiable vector field satisfying property (@) from the previous problem. Show that whenever & is a piecewise smooth, simple, closed curve we have Q Fide - Fady = 0 = Q F2dx + Fidy. Hint: Apply Green's Theorem to the region D bounded by . . Let 9 be the unit disc x2 + y2