Divide $ \, 7-9i \, $ by $ \, 4-3i \, $ to get $\,\, \dfrac{11-3i}{5} $.
( view steps )Divide $ \, 3-5i \, $ by $ \, 2i \, $ to get $\,\, \dfrac{-5-3i}{2} $.
( view steps )

Add $ \dfrac{11-3i}{5} $ and $ \dfrac{-5-3i}{2} $ to get $ \dfrac{ \color{purple}{ -21i-3 } }{ 10 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ 2 }$ and the second by $\color{blue}{ 5 }$.

$$ \begin{aligned} \frac{11-3i}{5} + \frac{-5-3i}{2} & = \frac{ \left( 11-3i \right) \cdot \color{blue}{ 2 }}{ 5 \cdot \color{blue}{ 2 }} + \frac{ \left( -5-3i \right) \cdot \color{blue}{ 5 }}{ 2 \cdot \color{blue}{ 5 }} = \\[1ex] &=\frac{ \color{purple}{ 22-6i } }{ 10 } + \frac{ \color{purple}{ -25-15i } }{ 10 }=\frac{ \color{purple}{ -21i-3 } }{ 10 } \end{aligned} $$