Question
Answer
$$4\cdot\dfrac{i}{6+3i}=\dfrac{8i+4}{15}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4 \cdot \frac{i}{6+3i}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4 \cdot \frac{1+2i}{15} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{8i+4}{15}\end{aligned} $$ | |
| ① | Divide $ \, i \, $ by $ \, 6+3i \, $ to get $\,\, \dfrac{1+2i}{15} $. ( view steps ) |
| ② | Multiply $4$ by $ \dfrac{1+2i}{15} $ to get $ \dfrac{8i+4}{15} $. Step 1: Write $ 4 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 4 \cdot \frac{1+2i}{15} & \xlongequal{\text{Step 1}} \frac{4}{\color{red}{1}} \cdot \frac{1+2i}{15} \xlongequal{\text{Step 2}} \frac{ 4 \cdot \left( 1+2i \right) }{ 1 \cdot 15 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4+8i }{ 15 } = \frac{8i+4}{15} \end{aligned} $$ |
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