Question
Answer
$$\dfrac{3-2i+2+4i}{-5+10i-(2+15i)}=\dfrac{-45+11i}{74}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3-2i+2+4i}{-5+10i-(2+15i)}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{2i+5}{-5+10i-2-15i} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{2i+5}{-5i-7} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-45+11i}{74}\end{aligned} $$ | |
| ① | Combine like terms: $$ \color{blue}{3} \color{red}{-2i} + \color{blue}{2} + \color{red}{4i} = \color{red}{2i} + \color{blue}{5} $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( 2+15i \right) = -2-15i $$ |
| ③ | Simplify denominator $$ \color{blue}{-5} + \color{red}{10i} \color{blue}{-2} \color{red}{-15i} = \color{red}{-5i} \color{blue}{-7} $$ |
| ④ | Divide $ \, 5+2i \, $ by $ \, -7-5i \, $ to get $\,\, \dfrac{-45+11i}{74} $. ( view steps ) |
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