Question
Answer
$$\dfrac{(50-100i)\cdot(250+500i)}{50-100i+250+500i}=\dfrac{62500}{400i+300}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{(50-100i)\cdot(250+500i)}{50-100i+250+500i}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{12500+25000i-25000i-50000i^2}{400i+300} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{12500+25000i-25000i+50000}{400i+300} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{62500}{400i+300}\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{50-100i}\right) $ by each term in $ \left( 250+500i\right) $. $$ \left( \color{blue}{50-100i}\right) \cdot \left( 250+500i\right) = 12500+ \cancel{25000i} -\cancel{25000i}-50000i^2 $$ |
| ② | Combine like terms: $$ \color{blue}{50} \color{red}{-100i} + \color{blue}{250} + \color{red}{500i} = \color{red}{400i} + \color{blue}{300} $$ |
| ③ | $$ -50000i^2 = -50000 \cdot (-1) = 50000 $$ |
| ④ | Simplify numerator $$ \color{blue}{12500} + \, \color{red}{ \cancel{25000i}} \, \, \color{red}{ -\cancel{25000i}} \,+ \color{blue}{50000} = \color{blue}{62500} $$ |
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