Subtract $3i$ from $ \dfrac{3}{7} $ to get $ \dfrac{ \color{purple}{ -21i+3 } }{ 7 }$.

Step 1: Write $ 3i $ 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 $\color{blue}{7}$.

$$ \begin{aligned} \frac{3}{7} -3i & \xlongequal{\text{Step 1}} \frac{3}{7} - \frac{3i}{\color{red}{1}} = \frac{ 3 }{ 7 } - \frac{ 3i \cdot \color{blue}{ 7 }}{ 1 \cdot \color{blue}{ 7 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 3 } }{ 7 } - \frac{ \color{purple}{ 21i } }{ 7 }=\frac{ \color{purple}{ -21i+3 } }{ 7 } \end{aligned} $$