Let C be the set of all complex numbers. Let S _ 1 = \ z ∈ C | |z –...

${S}_{1}: {\left|z - 3 - 2i\right|}^{2} = 8$

$⇒ \left|z - 3 - 2i\right| = 2\sqrt{2}$

$⇒ {\left(x - 3\right)}^{2} + {\left(y - 2\right)}^{2} = {\left(2\sqrt{2}\right)}^{2}$ (Put $z = x + iy$)

${S}_{2}: x \ge 5$

${S}_{3}: \left|z - \overset{¯}{z}\right| \ge 8$ (put $z = x + iy$)

$⇒ \left|2iy\right| \ge 8$

$⇒ 2\left|y\right| \ge 8 ∴ y \ge 4, y \le - 4$

So, the required diagram is

Hence, $n\left({S}_{1} \cap {S}_{2} \cap {S}_{3}\right) = 1$