Divide $ \, 42+42i \, $ by $ \, 7-10i \, $ to get $\,\, \dfrac{-126+714i}{149} $.
( view steps )

Add $ \dfrac{-126+714i}{149} $ and $ 2i $ to get $ \dfrac{ \color{purple}{ 1012i-126 } }{ 149 }$.

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 $\color{blue}{149}$.

$$ \begin{aligned} \frac{-126+714i}{149} +2i & \xlongequal{\text{Step 1}} \frac{-126+714i}{149} + \frac{2i}{\color{red}{1}} = \frac{ -126+714i }{ 149 } + \frac{ 2i \cdot \color{blue}{ 149 }}{ 1 \cdot \color{blue}{ 149 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -126+714i } }{ 149 } + \frac{ \color{purple}{ 298i } }{ 149 }=\frac{ \color{purple}{ 1012i-126 } }{ 149 } \end{aligned} $$