(a) Inside/on the circle centred at (4,2), radius 3. Writing z=x+iy, \(x^2+y^2\ge(10-x)^2+y^2\) gives x≥5, so retain its right-hand cap.

(b) The maximum argument is at the upper intersection with x=5. From \((5-4)^2+(y-2)^2=9\), \(y=2+2\sqrt2\). Therefore \(\arg z=\tan^{-1}[(2+2\sqrt2)/5]=0.768\text{ rad}\) (44.0°).