Question
Answer
$$80\cdot\dfrac{-i\cdot10.61}{80-i\cdot10.61}=\dfrac{-640i+80}{65}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}80 \cdot \frac{-i\cdot10.61}{80-i\cdot10.61}& \xlongequal{ }80 \cdot \frac{-i\cdot10.61}{80-10i} \xlongequal{ } \\[1 em] & \xlongequal{ }80 \cdot \frac{-10i}{80-10i} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}80 \cdot \frac{1-8i}{65} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-640i+80}{65}\end{aligned} $$ | |
| ① | Divide $ \, -10i \, $ by $ \, 80-10i \, $ to get $\,\, \dfrac{1-8i}{65} $. ( view steps ) |
| ② | Multiply $80$ by $ \dfrac{1-8i}{65} $ to get $ \dfrac{-640i+80}{65} $. Step 1: Write $ 80 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 80 \cdot \frac{1-8i}{65} & \xlongequal{\text{Step 1}} \frac{80}{\color{red}{1}} \cdot \frac{1-8i}{65} \xlongequal{\text{Step 2}} \frac{ 80 \cdot \left( 1-8i \right) }{ 1 \cdot 65 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 80-640i }{ 65 } = \frac{-640i+80}{65} \end{aligned} $$ |
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