Question
Answer
$$\dfrac{(10+5i)\cdot(10-5i)}{50-50i}=\dfrac{125}{50-50i}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{(10+5i)\cdot(10-5i)}{50-50i}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{100-50i+50i-25i^2}{50-50i} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{100-50i+50i+25}{50-50i} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{125}{50-50i}\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{10+5i}\right) $ by each term in $ \left( 10-5i\right) $. $$ \left( \color{blue}{10+5i}\right) \cdot \left( 10-5i\right) = 100 -\cancel{50i}+ \cancel{50i}-25i^2 $$ |
| ② | $$ -25i^2 = -25 \cdot (-1) = 25 $$ |
| ③ | Simplify numerator $$ \color{blue}{100} \, \color{red}{ -\cancel{50i}} \,+ \, \color{red}{ \cancel{50i}} \,+ \color{blue}{25} = \color{blue}{125} $$ |
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