Add $2$ and $ \dfrac{i}{1} $ to get $ \dfrac{i+2}{1} $.

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

Step 2: To add expressions with the same denominators, we add the numerators and write the result over the common denominator.

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

Add $ \dfrac{i+2}{1} $ and $ i $ to get $ \dfrac{2i+2}{1} $.

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

Step 2: To add expressions with the same denominators, we add the numerators and write the result over the common denominator.

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