Question
Answer
$$30\cdot\dfrac{4-40i}{40i}=\dfrac{-30i-300}{10}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}30 \cdot \frac{4-40i}{40i}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}30 \cdot \frac{-10-i}{10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-30i-300}{10}\end{aligned} $$ | |
| ① | Divide $ \, 4-40i \, $ by $ \, 40i \, $ to get $\,\, \dfrac{-10-i}{10} $. ( view steps ) |
| ② | Multiply $30$ by $ \dfrac{-10-i}{10} $ to get $ \dfrac{-30i-300}{10} $. Step 1: Write $ 30 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 30 \cdot \frac{-10-i}{10} & \xlongequal{\text{Step 1}} \frac{30}{\color{red}{1}} \cdot \frac{-10-i}{10} \xlongequal{\text{Step 2}} \frac{ 30 \cdot \left( -10-i \right) }{ 1 \cdot 10 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -300-30i }{ 10 } = \frac{-30i-300}{10} \end{aligned} $$ |
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