Multiply $ \dfrac{3}{4} $ by $ i $ to get $ \dfrac{ 3i }{ 4 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{3}{4} \cdot i & \xlongequal{\text{Step 1}} \frac{3}{4} \cdot \frac{i}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 3 \cdot i }{ 4 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 3i }{ 4 } \end{aligned} $$

Multiply $ \dfrac{5}{4} $ by $ i $ to get $ \dfrac{ 5i }{ 4 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{5}{4} \cdot i & \xlongequal{\text{Step 1}} \frac{5}{4} \cdot \frac{i}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5 \cdot i }{ 4 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 5i }{ 4 } \end{aligned} $$

Subtract $ \dfrac{3i}{4} $ from $ 7 $ to get $ \dfrac{ \color{purple}{ -3i+28 } }{ 4 }$.

Step 1: Write $ 7 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 4 }$.

$$ \begin{aligned} 7- \frac{3i}{4} & \xlongequal{\text{Step 1}} \frac{7}{\color{red}{1}} - \frac{3i}{4} = \frac{ 7 \cdot \color{blue}{ 4 }}{ 1 \cdot \color{blue}{ 4 }} - \frac{ 3i }{ 4 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 28 } }{ 4 } - \frac{ \color{purple}{ 3i } }{ 4 }=\frac{ \color{purple}{ -3i+28 } }{ 4 } \end{aligned} $$

Add $10$ and $ \dfrac{5i}{4} $ to get $ \dfrac{ \color{purple}{ 5i+40 } }{ 4 }$.

Step 1: Write $ 10 $ 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 first fraction by $\color{blue}{ 4 }$.

$$ \begin{aligned} 10+ \frac{5i}{4} & \xlongequal{\text{Step 1}} \frac{10}{\color{red}{1}} + \frac{5i}{4} = \frac{ 10 \cdot \color{blue}{ 4 }}{ 1 \cdot \color{blue}{ 4 }} + \frac{ 5i }{ 4 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 40 } }{ 4 } + \frac{ \color{purple}{ 5i } }{ 4 }=\frac{ \color{purple}{ 5i+40 } }{ 4 } \end{aligned} $$

Subtract $ \dfrac{5i+40}{4} $ from $ \dfrac{-3i+28}{4} $ to get $ \dfrac{-8i-12}{4} $.

To subtract expressions with the same denominators, we subtract the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{-3i+28}{4} - \frac{5i+40}{4} & = \frac{-3i+28}{\color{blue}{4}} - \frac{5i+40}{\color{blue}{4}} =\frac{ -3i+28 - \left( 5i+40 \right) }{ \color{blue}{ 4 }} = \\[1ex] &= \frac{-8i-12}{4} \end{aligned} $$