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Answer

$$\frac{42.43+42.43i}{75-10i}+2i=\frac{3004i+546}{1145}$$

Explanation

Tap the blue circles to see an explanation.

$$ \begin{aligned}\frac{42.43+42.43i}{75-10i}+2i& \xlongequal{ }\frac{42.43+42i}{75-10i}+2i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{546+714i}{1145}+2i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{3004i+546}{1145}\end{aligned} $$
①
Divide $ \, 42+42i \, $ by $ \, 75-10i \, $ to get $\,\, \dfrac{546+714i}{1145} $.
( view steps )
②

Add $ \dfrac{546+714i}{1145} $ and $ 2i $ to get $ \dfrac{ \color{purple}{ 3004i+546 } }{ 1145 }$.

Step 1: Write $ 2i $ 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 $\color{blue}{1145}$.

$$ \begin{aligned} \frac{546+714i}{1145} +2i & \xlongequal{\text{Step 1}} \frac{546+714i}{1145} + \frac{2i}{\color{red}{1}} = \frac{ 546+714i }{ 1145 } + \frac{ 2i \cdot \color{blue}{ 1145 }}{ 1 \cdot \color{blue}{ 1145 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 546+714i } }{ 1145 } + \frac{ \color{purple}{ 2290i } }{ 1145 }=\frac{ \color{purple}{ 3004i+546 } }{ 1145 } \end{aligned} $$
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