Question
Answer
$$10\cdot\dfrac{25+25i}{75+25i}=\dfrac{10i+20}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}10 \cdot \frac{25+25i}{75+25i}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}10 \cdot \frac{2+i}{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{10i+20}{5}\end{aligned} $$ | |
| ① | Divide $ \, 25+25i \, $ by $ \, 75+25i \, $ to get $\,\, \dfrac{2+i}{5} $. ( view steps ) |
| ② | Multiply $10$ by $ \dfrac{2+i}{5} $ to get $ \dfrac{10i+20}{5} $. Step 1: Write $ 10 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 10 \cdot \frac{2+i}{5} & \xlongequal{\text{Step 1}} \frac{10}{\color{red}{1}} \cdot \frac{2+i}{5} \xlongequal{\text{Step 2}} \frac{ 10 \cdot \left( 2+i \right) }{ 1 \cdot 5 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 20+10i }{ 5 } = \frac{10i+20}{5} \end{aligned} $$ |
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