Use the distributive property.

Multiply $ \color{blue}{80} $ by $ \left( 1+i\right) $ $$ \color{blue}{80} \cdot \left( 1+i\right) = 80+80i $$

Combine like terms:

$$ \color{blue}{v} -10+ \color{blue}{v} = \color{blue}{2v} -10 $$

Multiply $2v-10$ by $ \dfrac{1}{80+80i} $ to get $ \dfrac{ v-5 }{ 40i+40 } $.

Step 1: Write $ 2v-10 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Factor numerators and denominators.

Step 3: Cancel common factors.

Step 4: Multiply numerators and denominators.

Step 5: Simplify numerator and denominator.

$$ \begin{aligned} 2v-10 \cdot \frac{1}{80+80i} & \xlongequal{\text{Step 1}} \frac{2v-10}{\color{red}{1}} \cdot \frac{1}{80+80i} \xlongequal{\text{Step 2}} \frac{ \left( v-5 \right) \cdot \color{blue}{2} }{ 1 } \cdot \frac{ 1 }{ \left( 40i+40 \right) \cdot \color{blue}{2} } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ v-5 }{ 1 } \cdot \frac{ 1 }{ 40i+40 } \xlongequal{\text{Step 4}} \frac{ \left( v-5 \right) \cdot 1 }{ 1 \cdot \left( 40i+40 \right) } = \\[1ex] & \xlongequal{\text{Step 5}} \frac{ v-5 }{ 40i+40 } \end{aligned} $$

Add $ \dfrac{v-5}{40i+40} $ and $ \dfrac{v-a}{-80i} $ to get $ \dfrac{ \color{purple}{ -40ai-40iv-40a+400i+40v } }{ -3200i^2-3200i }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ -80i }$ and the second by $\color{blue}{ 40i+40 }$.

$$ \begin{aligned} \frac{v-5}{40i+40} + \frac{v-a}{-80i} & = \frac{ \left( v-5 \right) \cdot \color{blue}{ \left( -80i \right) }}{ \left( 40i+40 \right) \cdot \color{blue}{ \left( -80i \right) }} + \frac{ \left( v-a \right) \cdot \color{blue}{ \left( 40i+40 \right) }}{ \left( -80i \right) \cdot \color{blue}{ \left( 40i+40 \right) }} = \\[1ex] &=\frac{ \color{purple}{ -80iv+400i } }{ -3200i^2-3200i } + \frac{ \color{purple}{ 40iv+40v-40ai-40a } }{ -3200i^2-3200i } = \\[1ex] &=\frac{ \color{purple}{ -40ai-40iv-40a+400i+40v } }{ -3200i^2-3200i } \end{aligned} $$

$$ -3200i^2 = -3200 \cdot (-1) = 3200 $$