Question
Answer
$$6\cdot8\cdot\dfrac{i}{6-8i}=\dfrac{144i-192}{50}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}6\cdot8 \cdot \frac{i}{6-8i}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}48 \cdot \frac{i}{6-8i} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}48 \cdot \frac{-4+3i}{50} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{144i-192}{50}\end{aligned} $$ | |
| ① | $$ 6 \cdot 8 = 48 $$ |
| ② | Divide $ \, i \, $ by $ \, 6-8i \, $ to get $\,\, \dfrac{-4+3i}{50} $. ( view steps ) |
| ③ | Multiply $48$ by $ \dfrac{-4+3i}{50} $ to get $ \dfrac{144i-192}{50} $. Step 1: Write $ 48 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 48 \cdot \frac{-4+3i}{50} & \xlongequal{\text{Step 1}} \frac{48}{\color{red}{1}} \cdot \frac{-4+3i}{50} \xlongequal{\text{Step 2}} \frac{ 48 \cdot \left( -4+3i \right) }{ 1 \cdot 50 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -192+144i }{ 50 } = \frac{144i-192}{50} \end{aligned} $$ |
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