Question
Answer
$$-i\cdot32\cdot\dfrac{50+50i}{-32i+50i+50}=\dfrac{6400-13600i}{353}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-i\cdot32 \cdot \frac{50+50i}{-32i+50i+50}& \xlongequal{ }-i\cdot32 \cdot \frac{50+50i}{18i+50} \xlongequal{ } \\[1 em] & \xlongequal{ }-i\cdot32 \cdot \frac{425+200i}{353} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-\frac{6400i^2+13600i}{353} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6400-13600i}{353}\end{aligned} $$ | |
| ① | Multiply $32i$ by $ \dfrac{425+200i}{353} $ to get $ \dfrac{6400i^2+13600i}{353} $. Step 1: Write $ 32i $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 32i \cdot \frac{425+200i}{353} & \xlongequal{\text{Step 1}} \frac{32i}{\color{red}{1}} \cdot \frac{425+200i}{353} \xlongequal{\text{Step 2}} \frac{ 32i \cdot \left( 425+200i \right) }{ 1 \cdot 353 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 13600i+6400i^2 }{ 353 } = \frac{6400i^2+13600i}{353} \end{aligned} $$ |
| ② | $$ -6400i^2 = -6400 \cdot (-1) = 6400 $$ |
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