Add $ \dfrac{4}{3} $ and $ i $ to get $ \dfrac{ \color{purple}{ 3i+4 } }{ 3 }$.

Step 1: Write $ i $ 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 $\color{blue}{3}$.

$$ \begin{aligned} \frac{4}{3} +i & \xlongequal{\text{Step 1}} \frac{4}{3} + \frac{i}{\color{red}{1}} = \frac{ 4 }{ 3 } + \frac{ i \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 4 } }{ 3 } + \frac{ \color{purple}{ 3i } }{ 3 }=\frac{ \color{purple}{ 3i+4 } }{ 3 } \end{aligned} $$