Question
Answer
$$(1392.7-1129.93i)\cdot\dfrac{25}{20\cdot25-500i}=\dfrac{2521+263i}{40}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(1392.7-1129.93i)\cdot\frac{25}{20\cdot25-500i}& \xlongequal{ }(1392.7-1129i)\cdot\frac{25}{20\cdot25-500i} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{-28225i+34800}{-500i+500} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{2521+263i}{40}\end{aligned} $$ | |
| ① | Multiply $1392-1129i$ by $ \dfrac{25}{500-500i} $ to get $ \dfrac{-28225i+34800}{-500i+500} $. Step 1: Write $ 1392-1129i $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 1392-1129i \cdot \frac{25}{500-500i} & \xlongequal{\text{Step 1}} \frac{1392-1129i}{\color{red}{1}} \cdot \frac{25}{500-500i} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( 1392-1129i \right) \cdot 25 }{ 1 \cdot \left( 500-500i \right) } \xlongequal{\text{Step 3}} \frac{ 34800-28225i }{ 500-500i } = \\[1ex] &= \frac{-28225i+34800}{-500i+500} \end{aligned} $$ |
| ② | Divide $ \, 34800-28225i \, $ by $ \, 500-500i \, $ to get $\,\, \dfrac{2521+263i}{40} $. ( view steps ) |
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