Add $ \dfrac{1157000}{10719-6595i} $ and $ 9 $ to get $ \dfrac{ \color{purple}{ -59355i+1253471 } }{ -6595i+10719 }$.

Step 1: Write $ 9 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{-6595i+10719}$.

$$ \begin{aligned} \frac{1157000}{10719-6595i} +9 & \xlongequal{\text{Step 1}} \frac{1157000}{10719-6595i} + \frac{9}{\color{red}{1}} = \frac{ 1157000 }{ 10719-6595i } + \frac{ 9 \cdot \color{blue}{ \left( -6595i+10719 \right) }}{ 1 \cdot \color{blue}{ \left( -6595i+10719 \right) }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 1157000 } }{ 10719-6595i } + \frac{ \color{purple}{ -59355i+96471 } }{ 10719-6595i } = \\[1ex] &=\frac{ \color{purple}{ -59355i+1253471 } }{ -6595i+10719 } \end{aligned} $$

Divide $ \, 1253471-59355i \, $ by $ \, 10719-6595i \, $ to get $\,\, \dfrac{5975541+3297500i}{68449} $.
( view steps )

Add $ \dfrac{5975541+3297500i}{68449} $ and $ 10i $ to get $ \dfrac{ \color{purple}{ 3981990i+5975541 } }{ 68449 }$.

Step 1: Write $ 10i $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{68449}$.

$$ \begin{aligned} \frac{5975541+3297500i}{68449} +10i & \xlongequal{\text{Step 1}} \frac{5975541+3297500i}{68449} + \frac{10i}{\color{red}{1}} = \frac{ 5975541+3297500i }{ 68449 } + \frac{ 10i \cdot \color{blue}{ 68449 }}{ 1 \cdot \color{blue}{ 68449 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 5975541+3297500i } }{ 68449 } + \frac{ \color{purple}{ 684490i } }{ 68449 }=\frac{ \color{purple}{ 3981990i+5975541 } }{ 68449 } \end{aligned} $$