Question
Answer
$$-120\cdot\dfrac{i}{50-120i}\cdot80=\dfrac{48000i-115200}{1690}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-120 \cdot \frac{i}{50-120i}\cdot80& \xlongequal{ }-120 \cdot \frac{-12+5i}{1690}\cdot80 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{600i-1440}{1690}\cdot80 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{48000i-115200}{1690}\end{aligned} $$ | |
| ① | Multiply $120$ by $ \dfrac{-12+5i}{1690} $ to get $ \dfrac{600i-1440}{1690} $. Step 1: Write $ 120 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 120 \cdot \frac{-12+5i}{1690} & \xlongequal{\text{Step 1}} \frac{120}{\color{red}{1}} \cdot \frac{-12+5i}{1690} \xlongequal{\text{Step 2}} \frac{ 120 \cdot \left( -12+5i \right) }{ 1 \cdot 1690 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -1440+600i }{ 1690 } = \frac{600i-1440}{1690} \end{aligned} $$ |
| ② | Multiply $ \dfrac{600i-1440}{1690} $ by $ 80 $ to get $ \dfrac{ 48000i-115200 }{ 1690 } $. Step 1: Write $ 80 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{600i-1440}{1690} \cdot 80 & \xlongequal{\text{Step 1}} \frac{600i-1440}{1690} \cdot \frac{80}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 600i-1440 \right) \cdot 80 }{ 1690 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 48000i-115200 }{ 1690 } \end{aligned} $$ |
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