Multiply $ \dfrac{1}{2} $ by $ i $ to get $ \dfrac{ i }{ 2 } $.

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.

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

Subtract $ \dfrac{i}{2} $ from $ 3 $ to get $ \dfrac{ \color{purple}{ -i+6 } }{ 2 }$.

Step 1: Write $ 3 $ 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 $\color{blue}{ 2 }$.

$$ \begin{aligned} 3- \frac{i}{2} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} - \frac{i}{2} = \frac{ 3 \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} - \frac{ i }{ 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 6 } }{ 2 } - \frac{ \color{purple}{ i } }{ 2 }=\frac{ \color{purple}{ -i+6 } }{ 2 } \end{aligned} $$

Multiply $ \dfrac{-i+6}{2} $ by $ -1+i $ to get $ \dfrac{-i^2+7i-6}{2} $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{-i+6}{2} \cdot -1+i & \xlongequal{\text{Step 1}} \frac{-i+6}{2} \cdot \frac{-1+i}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( -i+6 \right) \cdot \left( -1+i \right) }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ i-i^2-6+6i }{ 2 } = \frac{-i^2+7i-6}{2} \end{aligned} $$

$$ -i^2 = -(-1) = 1 $$

Simplify numerator

$$ \color{blue}{1} +7i \color{blue}{-6} = 7i \color{blue}{-5} $$