Multiply $3$ by $ \dfrac{i}{5} $ to get $ \dfrac{ 3i }{ 5 } $.

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.

$$ \begin{aligned} 3 \cdot \frac{i}{5} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} \cdot \frac{i}{5} \xlongequal{\text{Step 2}} \frac{ 3 \cdot i }{ 1 \cdot 5 } \xlongequal{\text{Step 3}} \frac{ 3i }{ 5 } \end{aligned} $$

Subtract $2i$ from $ \dfrac{3i}{5} $ to get $ \dfrac{ \color{purple}{ -7i } }{ 5 }$.

Step 1: Write $ 2i $ 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 $\color{blue}{5}$.

$$ \begin{aligned} \frac{3i}{5} -2i & \xlongequal{\text{Step 1}} \frac{3i}{5} - \frac{2i}{\color{red}{1}} = \frac{ 3i }{ 5 } - \frac{ 2i \cdot \color{blue}{ 5 }}{ 1 \cdot \color{blue}{ 5 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 3i } }{ 5 } - \frac{ \color{purple}{ 10i } }{ 5 }=\frac{ \color{purple}{ -7i } }{ 5 } \end{aligned} $$