. Suppose that F(x, y) = (Fi(x, y) , F2(x, y) ) is a twice continuously differentiable vector field with the property that OF1 OF2 OF OF2 (*) and Ox ay ay Ox Show that both Fi and F2 are harmonic, i.e., AF1 = 0 = AF2, where A = 22 22 dyz . . 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 Fidx - F2dy = 0 = Q F2 dx + Fidy. Hint: Apply Green's Theorem to the region D bounded by C