Add $ \dfrac{5}{2} $ and $ 2i $ to get $ \dfrac{ \color{purple}{ 4i+5 } }{ 2 }$.

Step 1: Write $ 2i $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{2}$.

$$ \begin{aligned} \frac{5}{2} +2i & \xlongequal{\text{Step 1}} \frac{5}{2} + \frac{2i}{\color{red}{1}} = \frac{ 5 }{ 2 } + \frac{ 2i \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 5 } }{ 2 } + \frac{ \color{purple}{ 4i } }{ 2 }=\frac{ \color{purple}{ 4i+5 } }{ 2 } \end{aligned} $$