Question
Answer
$$\dfrac{40+30i+60}{40+30i-60}=\dfrac{-11-36i}{13}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{40+30i+60}{40+30i-60}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{30i+100}{40+30i-60} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{30i+100}{30i-20} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-11-36i}{13}\end{aligned} $$ | |
| ① | Simplify numerator $$ \color{blue}{40} +30i+ \color{blue}{60} = 30i+ \color{blue}{100} $$ |
| ② | Simplify denominator $$ \color{blue}{40} +30i \color{blue}{-60} = 30i \color{blue}{-20} $$ |
| ③ | Divide $ \, 100+30i \, $ by $ \, -20+30i \, $ to get $\,\, \dfrac{-11-36i}{13} $. ( view steps ) |
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