Add $ \dfrac{1}{0+i} $ and $ \dfrac{2}{3+2i} $ to get $ \dfrac{ \color{purple}{ 4i+3 } }{ 2i^2+3i }$.

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}{ 2i+3 }$ and the second by $\color{blue}{ i }$.

$$ \begin{aligned} \frac{1}{0+i} + \frac{2}{3+2i} & = \frac{ 1 \cdot \color{blue}{ \left( 2i+3 \right) }}{ \left( 0+i \right) \cdot \color{blue}{ \left( 2i+3 \right) }} + \frac{ 2 \cdot \color{blue}{ i }}{ \left( 3+2i \right) \cdot \color{blue}{ i }} = \\[1ex] &=\frac{ \color{purple}{ 2i+3 } }{ 0i0+2i^2+3i } + \frac{ \color{purple}{ 2i } }{ 0i0+2i^2+3i }=\frac{ \color{purple}{ 4i+3 } }{ 2i^2+3i } \end{aligned} $$

$$ 2i^2 = 2 \cdot (-1) = -2 $$

Divide $ \, 3+4i \, $ by $ \, -2+3i \, $ to get $\,\, \dfrac{6-17i}{13} $.
( view steps )