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.

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

Subtract $ \dfrac{3i}{4} $ from $ \dfrac{1}{4} $ to get $ \dfrac{-3i+1}{4} $.

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

$$ \begin{aligned} \frac{1}{4} - \frac{3i}{4} & = \frac{1}{\color{blue}{4}} - \frac{3i}{\color{blue}{4}} =\frac{ 1 - 3i }{ \color{blue}{ 4 }} = \\[1ex] &= \frac{-3i+1}{4} \end{aligned} $$

Multiply $ \dfrac{-3i+1}{4} $ by $ 1 $ to get $ \dfrac{ -3i+1 }{ 4 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{-3i+1}{4} \cdot 1 & \xlongequal{\text{Step 1}} \frac{-3i+1}{4} \cdot \frac{1}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( -3i+1 \right) \cdot 1 }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -3i+1 }{ 4 } \end{aligned} $$

Multiply $ \dfrac{-3i+1}{4} $ by $ i $ to get $ \dfrac{ -3i^2+i }{ 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.

$$ \begin{aligned} \frac{-3i+1}{4} \cdot i & \xlongequal{\text{Step 1}} \frac{-3i+1}{4} \cdot \frac{i}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( -3i+1 \right) \cdot i }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -3i^2+i }{ 4 } \end{aligned} $$

$$ -3i^2 = -3 \cdot (-1) = 3 $$