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Question

Answer

$$\dfrac{4+5i}{2}+\dfrac{8-5i}{14}=\dfrac{30i+36}{14}$$

Explanation
$$ \begin{aligned}\frac{4+5i}{2}+\frac{8-5i}{14}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{30i+36}{14}\end{aligned} $$
①

Add $ \dfrac{4+5i}{2} $ and $ \dfrac{8-5i}{14} $ to get $ \dfrac{ \color{purple}{ 30i+36 } }{ 14 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 7 }$.

$$ \begin{aligned} \frac{4+5i}{2} + \frac{8-5i}{14} & = \frac{ \left( 4+5i \right) \cdot \color{blue}{ 7 }}{ 2 \cdot \color{blue}{ 7 }} + \frac{ 8-5i }{ 14 } = \\[1ex] &=\frac{ \color{purple}{ 28+35i } }{ 14 } + \frac{ \color{purple}{ 8-5i } }{ 14 }=\frac{ \color{purple}{ 30i+36 } }{ 14 } \end{aligned} $$
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