{c}

The disc is a <closed set> and is bounded in the <complex plane>, so it is \b[compact] by the <Heine-Borel theorem>. It is <convex>: the <triangle inequality> gives $|(1-t)z_0+tz_1|\leq2$ for all $t\in[0,1]$ when both endpoints lie in it. Straight segments therefore supply paths, so it is <path-connected> and hence \b[connected].

Solution

Past exam of the algebra, analysis and differential equations 1 course of the University of Oxford / 2011 / 4 / b / Solution

 Solution (source code)