Add $ \dfrac{1}{4} $ and $ 5i $ to get $ \dfrac{ \color{purple}{ 20i+1 } }{ 4 }$.

Step 1: Write $ 5i $ 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 $\color{blue}{4}$.

$$ \begin{aligned} \frac{1}{4} +5i & \xlongequal{\text{Step 1}} \frac{1}{4} + \frac{5i}{\color{red}{1}} = \frac{ 1 }{ 4 } + \frac{ 5i \cdot \color{blue}{ 4 }}{ 1 \cdot \color{blue}{ 4 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 1 } }{ 4 } + \frac{ \color{purple}{ 20i } }{ 4 }=\frac{ \color{purple}{ 20i+1 } }{ 4 } \end{aligned} $$