Explanation

(b)
Since, $2 + i\sqrt{3}$ is a root of the equation $x^{2} + px + q = 0$, then the other root will be $2 - i\sqrt{3}$
$\therefore\ \ 2 + i\sqrt{3} + 2 - i\sqrt{3} = - p$
$\Rightarrow \ \ p = - 4$
And $\left( 2 + i\sqrt{3} \right)\left( 2 - i\sqrt{3} = q \right)$
$\Rightarrow \ \ \ \ \ q = 7$
$\therefore$ The value of $(p,\ q)$ is $( - 4,\ 7)$