Question
Answer
$$5\cdot\dfrac{i}{2+i}=2i+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5 \cdot \frac{i}{2+i}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}5 \cdot \frac{1+2i}{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2i+1\end{aligned} $$ | |
| ① | Divide $ \, i \, $ by $ \, 2+i \, $ to get $\,\, \dfrac{1+2i}{5} $. ( view steps ) |
| ② | Multiply $5$ by $ \dfrac{1+2i}{5} $ to get $ 1+2i$. Step 1: Write $ 5 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Cancel $ \color{blue}{ 5 } $ in first and second fraction. Step 3: Multiply numerators and denominators. Step 4: Simplify numerator and denominator. $$ \begin{aligned} 5 \cdot \frac{1+2i}{5} & \xlongequal{\text{Step 1}} \frac{5}{\color{red}{1}} \cdot \frac{1+2i}{5} \xlongequal{\text{Step 2}} \frac{\color{blue}{1}}{1} \cdot \frac{1+2i}{\color{blue}{1}} = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 1 \cdot \left( 1+2i \right) }{ 1 \cdot 1 } \xlongequal{\text{Step 4}} \frac{ 1+2i }{ 1 } = \frac{2i+1}{1} =1+2i \end{aligned} $$ |
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