Question
Answer
$$2\cdot\dfrac{i}{1+i}=i+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2 \cdot \frac{i}{1+i}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2 \cdot \frac{1+i}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}i+1\end{aligned} $$ | |
| ① | Divide $ \, i \, $ by $ \, 1+i \, $ to get $\,\, \dfrac{1+i}{2} $. ( view steps ) |
| ② | Multiply $2$ by $ \dfrac{1+i}{2} $ to get $ 1+i$. Step 1: Write $ 2 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Cancel $ \color{blue}{ 2 } $ in first and second fraction. Step 3: Multiply numerators and denominators. Step 4: Simplify numerator and denominator. $$ \begin{aligned} 2 \cdot \frac{1+i}{2} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{1+i}{2} \xlongequal{\text{Step 2}} \frac{\color{blue}{1}}{1} \cdot \frac{1+i}{\color{blue}{1}} = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 1 \cdot \left( 1+i \right) }{ 1 \cdot 1 } \xlongequal{\text{Step 4}} \frac{ 1+i }{ 1 } = \frac{i+1}{1} =1+i \end{aligned} $$ |
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