Draw the disk centred at \((0,3)\) with radius 2. The argument is measured from \((1,2)\), so draw rays from this point at angles \(\pi/4\) and \(3\pi/4\) to the positive real direction. Shade the part of the disk between the upward rays: in coordinates it is \[x^2+(y-3)^2\le4,\qquad y-2\ge|x-1|.\] The circle and rays are included. The apex \((1,2)\) itself is excluded because \(\arg0\) is undefined.