Answer
$$2\cdot\frac{i}{10+2i}=\frac{10i+2}{52}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2 \cdot \frac{i}{10+2i}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2 \cdot \frac{1+5i}{52} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{10i+2}{52}\end{aligned} $$ | |
| ① | Divide $ \, i \, $ by $ \, 10+2i \, $ to get $\,\, \dfrac{1+5i}{52} $. ( view steps ) |
| ② | Multiply $2$ by $ \dfrac{1+5i}{52} $ to get $ \dfrac{10i+2}{52} $. Step 1: Write $ 2 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 2 \cdot \frac{1+5i}{52} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{1+5i}{52} \xlongequal{\text{Step 2}} \frac{ 2 \cdot \left( 1+5i \right) }{ 1 \cdot 52 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2+10i }{ 52 } = \frac{10i+2}{52} \end{aligned} $$ |
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