Question
Answer
$$50\cdot\dfrac{100-14i}{86+72i}=\dfrac{-105050i+94900}{3145}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}50 \cdot \frac{100-14i}{86+72i}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}50 \cdot \frac{1898-2101i}{3145} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-105050i+94900}{3145}\end{aligned} $$ | |
| ① | Divide $ \, 100-14i \, $ by $ \, 86+72i \, $ to get $\,\, \dfrac{1898-2101i}{3145} $. ( view steps ) |
| ② | Multiply $50$ by $ \dfrac{1898-2101i}{3145} $ to get $ \dfrac{-105050i+94900}{3145} $. Step 1: Write $ 50 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 50 \cdot \frac{1898-2101i}{3145} & \xlongequal{\text{Step 1}} \frac{50}{\color{red}{1}} \cdot \frac{1898-2101i}{3145} \xlongequal{\text{Step 2}} \frac{ 50 \cdot \left( 1898-2101i \right) }{ 1 \cdot 3145 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 94900-105050i }{ 3145 } = \frac{-105050i+94900}{3145} \end{aligned} $$ |
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