Divide $ \, -3+2i \, $ by $ \, 4+i \, $ to get $\,\, \dfrac{-10+11i}{17} $.
( view steps )

Subtract $ \dfrac{-10+11i}{17} $ from $ i+2 $ to get $ \dfrac{ \color{purple}{ 6i+44 } }{ 17 }$.

Step 1: Write $ i+2 $ 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 $\color{blue}{ 17 }$.

$$ \begin{aligned} i+2- \frac{-10+11i}{17} & \xlongequal{\text{Step 1}} \frac{i+2}{\color{red}{1}} - \frac{-10+11i}{17} = \frac{ \left( i+2 \right) \cdot \color{blue}{ 17 }}{ 1 \cdot \color{blue}{ 17 }} - \frac{ -10+11i }{ 17 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 17i+34 } }{ 17 } - \frac{ \color{purple}{ -10+11i } }{ 17 }=\frac{ \color{purple}{ 17i+34 - \left( -10+11i \right) } }{ 17 } = \\[1ex] &=\frac{ \color{purple}{ 6i+44 } }{ 17 } \end{aligned} $$