Question
Answer
$$3\cdot125.7\cdot\dfrac{i}{10+(125.7-0.08)i}=\dfrac{750i+9375}{3145}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3\cdot125.7 \cdot \frac{i}{10+(125.7-0.08)i}& \xlongequal{ }375 \cdot \frac{i}{10+(125.7-0.08)i} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}375 \cdot \frac{i}{10+125i+0i} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}375 \cdot \frac{i}{10+125i} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}375 \cdot \frac{25+2i}{3145} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{750i+9375}{3145}\end{aligned} $$ | |
| ① | $$ \left( \color{blue}{1250}\right) \cdot i = 125i0i $$ |
| ② | Combine like terms: $$ \color{blue}{125i} \color{blue}{0i} = \color{blue}{125i} $$ |
| ③ | Divide $ \, i \, $ by $ \, 10+125i \, $ to get $\,\, \dfrac{25+2i}{3145} $. ( view steps ) |
| ④ | Multiply $375$ by $ \dfrac{25+2i}{3145} $ to get $ \dfrac{750i+9375}{3145} $. Step 1: Write $ 375 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 375 \cdot \frac{25+2i}{3145} & \xlongequal{\text{Step 1}} \frac{375}{\color{red}{1}} \cdot \frac{25+2i}{3145} \xlongequal{\text{Step 2}} \frac{ 375 \cdot \left( 25+2i \right) }{ 1 \cdot 3145 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 9375+750i }{ 3145 } = \frac{750i+9375}{3145} \end{aligned} $$ |
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