Divide $ \, 3+4i \, $ by $ \, 5-2i \, $ to get $\,\, \dfrac{7+26i}{29} $.
( view steps )

Subtract $2i$ from $ \dfrac{7+26i}{29} $ to get $ \dfrac{ \color{purple}{ -32i+7 } }{ 29 }$.

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 $\color{blue}{29}$.

$$ \begin{aligned} \frac{7+26i}{29} -2i & \xlongequal{\text{Step 1}} \frac{7+26i}{29} - \frac{2i}{\color{red}{1}} = \frac{ 7+26i }{ 29 } - \frac{ 2i \cdot \color{blue}{ 29 }}{ 1 \cdot \color{blue}{ 29 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 7+26i } }{ 29 } - \frac{ \color{purple}{ 58i } }{ 29 }=\frac{ \color{purple}{ -32i+7 } }{ 29 } \end{aligned} $$