Multiply each term of $ \left( \color{blue}{2+4i}\right) $ by each term in $ \left( -3-i\right) $.

$$ \left( \color{blue}{2+4i}\right) \cdot \left( -3-i\right) = -6-2i-12i-4i^2 $$

Combine like terms:

$$ -6 \color{blue}{-2i} \color{blue}{-12i} -4i^2 = -4i^2 \color{blue}{-14i} -6 $$

$$ -4i^2 = -4 \cdot (-1) = 4 $$

Combine like terms:

$$ \color{blue}{4} -14i \color{blue}{-6} = -14i \color{blue}{-2} $$

Remove the parentheses by changing the sign of each term within them.

$$ - \left( -14i-2 \right) = 14i+2 $$

Combine like terms:

$$ \color{blue}{1} \color{red}{-4i} + \color{red}{14i} + \color{blue}{2} = \color{red}{10i} + \color{blue}{3} $$

Subtract $1$ from $ \dfrac{10i+3}{4} $ to get $ \dfrac{ \color{purple}{ 10i-1 } }{ 4 }$.

Step 1: Write $ 1 $ 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 $\color{blue}{4}$.

$$ \begin{aligned} \frac{10i+3}{4} -1 & \xlongequal{\text{Step 1}} \frac{10i+3}{4} - \frac{1}{\color{red}{1}} = \frac{ 10i+3 }{ 4 } - \frac{ 1 \cdot \color{blue}{ 4 }}{ 1 \cdot \color{blue}{ 4 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 10i+3 } }{ 4 } - \frac{ \color{purple}{ 4 } }{ 4 }=\frac{ \color{purple}{ 10i-1 } }{ 4 } \end{aligned} $$