Question
Answer
$$2\cdot\dfrac{i}{8+5i}=\dfrac{16i+10}{89}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2 \cdot \frac{i}{8+5i}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2 \cdot \frac{5+8i}{89} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{16i+10}{89}\end{aligned} $$ | |
| ① | Divide $ \, i \, $ by $ \, 8+5i \, $ to get $\,\, \dfrac{5+8i}{89} $. ( view steps ) |
| ② | Multiply $2$ by $ \dfrac{5+8i}{89} $ to get $ \dfrac{16i+10}{89} $. 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. $$ \begin{aligned} 2 \cdot \frac{5+8i}{89} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{5+8i}{89} \xlongequal{\text{Step 2}} \frac{ 2 \cdot \left( 5+8i \right) }{ 1 \cdot 89 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 10+16i }{ 89 } = \frac{16i+10}{89} \end{aligned} $$ |
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