I understand that the curl of a vector field $\textbf{F}$ being zero means that the field is conservative if its domain is simply connected. This was demonstrated in part a where I showed that the line integral over the unit circle was $-2\pi$. (b) explains how why a(ii) was $0$, as the field is conservative in this domain which IS simply connected. However after having found the answer to (b) I am not at all sure how to proceed for (c), as I cannot see how the answer I have just calculated is insufficient. I know that the vector field being undefined for $(x,y) = (0,0)$ means that there is in effect a "vertical line" through the origin where the field is undefined, but what would be a sufficient way to show this?