Multiply $3$ by $ \dfrac{i}{10} $ to get $ \dfrac{ 3i }{ 10 } $.

Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Subtract $ \dfrac{i}{5} $ from $ 3 $ to get $ \dfrac{ \color{purple}{ -i+15 } }{ 5 }$.

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 $\color{blue}{ 5 }$.

$$ \begin{aligned} 3- \frac{i}{5} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} - \frac{i}{5} = \frac{ 3 \cdot \color{blue}{ 5 }}{ 1 \cdot \color{blue}{ 5 }} - \frac{ i }{ 5 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 15 } }{ 5 } - \frac{ \color{purple}{ i } }{ 5 }=\frac{ \color{purple}{ -i+15 } }{ 5 } \end{aligned} $$

Add $ \dfrac{-3i}{10} $ and $ \dfrac{8}{5} $ to get $ \dfrac{ \color{purple}{ -3i+16 } }{ 10 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{2}$.

$$ \begin{aligned} \frac{-3i}{10} + \frac{8}{5} & = \frac{ -3i }{ 10 } + \frac{ 8 \cdot \color{blue}{ 2 }}{ 5 \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ -3i } }{ 10 } + \frac{ \color{purple}{ 16 } }{ 10 }=\frac{ \color{purple}{ -3i+16 } }{ 10 } \end{aligned} $$

Subtract $ \dfrac{i}{5} $ from $ 3 $ to get $ \dfrac{ \color{purple}{ -i+15 } }{ 5 }$.

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 $\color{blue}{ 5 }$.

$$ \begin{aligned} 3- \frac{i}{5} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} - \frac{i}{5} = \frac{ 3 \cdot \color{blue}{ 5 }}{ 1 \cdot \color{blue}{ 5 }} - \frac{ i }{ 5 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 15 } }{ 5 } - \frac{ \color{purple}{ i } }{ 5 }=\frac{ \color{purple}{ -i+15 } }{ 5 } \end{aligned} $$

Subtract $ \dfrac{-i+15}{5} $ from $ \dfrac{-3i+16}{10} $ to get $ \dfrac{ \color{purple}{ -i-14 } }{ 10 }$.

To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{2}$.

$$ \begin{aligned} \frac{-3i+16}{10} - \frac{-i+15}{5} & = \frac{ -3i+16 }{ 10 } - \frac{ \left( -i+15 \right) \cdot \color{blue}{ 2 }}{ 5 \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ -3i+16 } }{ 10 } - \frac{ \color{purple}{ -2i+30 } }{ 10 }=\frac{ \color{purple}{ -3i+16 - \left( -2i+30 \right) } }{ 10 } = \\[1ex] &=\frac{ \color{purple}{ -i-14 } }{ 10 } \end{aligned} $$