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