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

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.

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

Multiply $ \dfrac{-i}{2} $ by $ qrst-13 $ to get $ \dfrac{ -iqrst+13i }{ 2 } $.

Step 1: Write $ qrst-13 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{-i}{2} \cdot qrst-13 & \xlongequal{\text{Step 1}} \frac{-i}{2} \cdot \frac{qrst-13}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( -i \right) \cdot \left( qrst-13 \right) }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -iqrst+13i }{ 2 } \end{aligned} $$

Subtract $-3$ from $ \dfrac{-iqrst+13i}{2} $ to get $ \dfrac{ \color{purple}{ -iqrst+13i+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 second fraction by $\color{blue}{2}$.

$$ \begin{aligned} \frac{-iqrst+13i}{2} --3 & \xlongequal{\text{Step 1}} \frac{-iqrst+13i}{2} - \frac{-3}{\color{red}{1}} = \frac{ -iqrst+13i }{ 2 } - \frac{ \left( -3 \right) \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -iqrst+13i } }{ 2 } - \frac{ \color{purple}{ -6 } }{ 2 }=\frac{ \color{purple}{ -iqrst+13i+6 } }{ 2 } \end{aligned} $$