Find area of mobility in Argand plane for variable z such that, $3 \le \left| z \right| \le 5$ & $\frac{\pi }{8} \le \arg z \le \frac{\pi }{4}$

The required area = shaded area in the figure = $\frac{1}{2}({5^2} - {3^2})\left( {\frac{\pi }{4} - \frac{\pi }{8}} \right)$

$ = \frac{1}{2} \times 16 \times \frac{\pi }{8} = \pi $ square unit.