This problem shows the need for simple connectedness in the if statement of Theorem C. Let F

Question:

This problem shows the need for simple connectedness in the "if" statement of Theorem C. Let F = (yi - xj) / (x2 + y2) on the set D = {(x, y): x2 + y2 ≠ 0}.
Show each of the following.
(a) The condition ∂M/∂y = ∂N/∂x holds on D.
(b) F is not conservative on D.