Question
Answer
$$\dfrac{1}{\dfrac{12+3i}{84.738-124.81i}}=\dfrac{5608}{435i+159}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{1}{\frac{12+3i}{84.738-124.81i}}& \xlongequal{ }\frac{1}{\frac{12+3i}{84.738-124i}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{1}{\frac{159+435i}{5608}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{5608}{435i+159}\end{aligned} $$ | |
| ① | Divide $ \, 12+3i \, $ by $ \, 84-124i \, $ to get $\,\, \dfrac{159+435i}{5608} $. ( view steps ) |
| ② | Divide $1$ by $ \dfrac{159+435i}{5608} $ to get $ \dfrac{5608}{435i+159} $. Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction. Step 2: Write $ 1 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 3: Multiply numerators and denominators. Step 4: Simplify numerator and denominator. $$ \begin{aligned} \frac{1}{ \frac{\color{blue}{159+435i}}{\color{blue}{5608}} } & \xlongequal{\text{Step 1}} 1 \cdot \frac{\color{blue}{5608}}{\color{blue}{159+435i}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{1}{\color{red}{1}} \cdot \frac{5608}{159+435i} \xlongequal{\text{Step 3}} \frac{ 1 \cdot 5608 }{ 1 \cdot \left( 159+435i \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ 5608 }{ 159+435i } = \frac{5608}{435i+159} \end{aligned} $$ |
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