Ans: A
$\begin{array}{cl}
& \dfrac{\beta^2 + 4}{\beta +2i} \\
= & \dfrac{\beta^2 + 4}{\beta + 2i} \times \dfrac{\beta – 2i}{\beta – 2i} \\
= & \dfrac{(\beta^2 + 4)(\beta – 2i)}{\beta^2 – (2i)^2} \\
= & \dfrac{(\beta^2 + 4)(\beta – 2i)}{\beta^2 +4} \\
= & \beta – 2i
\end{array}$
$\begin{array}{cl}
& \dfrac{\beta^2 + 4}{\beta +2i} \\
= & \dfrac{\beta^2 + 4}{\beta + 2i} \times \dfrac{\beta – 2i}{\beta – 2i} \\
= & \dfrac{(\beta^2 + 4)(\beta – 2i)}{\beta^2 – (2i)^2} \\
= & \dfrac{(\beta^2 + 4)(\beta – 2i)}{\beta^2 +4} \\
= & \beta – 2i
\end{array}$
