Question
Answer
$$3\cdot\dfrac{i}{2+3i}=\dfrac{6i+9}{13}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3 \cdot \frac{i}{2+3i}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3 \cdot \frac{3+2i}{13} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6i+9}{13}\end{aligned} $$ | |
| ① | Divide $ \, i \, $ by $ \, 2+3i \, $ to get $\,\, \dfrac{3+2i}{13} $. ( view steps ) |
| ② | Multiply $3$ by $ \dfrac{3+2i}{13} $ to get $ \dfrac{6i+9}{13} $. Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 3 \cdot \frac{3+2i}{13} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} \cdot \frac{3+2i}{13} \xlongequal{\text{Step 2}} \frac{ 3 \cdot \left( 3+2i \right) }{ 1 \cdot 13 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 9+6i }{ 13 } = \frac{6i+9}{13} \end{aligned} $$ |
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