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

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

$$ i^2 = -1 $$

Subtract $3$ from $ \dfrac{-1+i}{2} $ to get $ \dfrac{ \color{purple}{ i-7 } }{ 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 second fraction by $\color{blue}{2}$.

$$ \begin{aligned} \frac{-1+i}{2} -3 & \xlongequal{\text{Step 1}} \frac{-1+i}{2} - \frac{3}{\color{red}{1}} = \frac{ -1+i }{ 2 } - \frac{ 3 \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -1+i } }{ 2 } - \frac{ \color{purple}{ 6 } }{ 2 }=\frac{ \color{purple}{ i-7 } }{ 2 } \end{aligned} $$