Question
Answer
$$\dfrac{5-10i}{3-i}\dfrac{3+i}{3+i}=\dfrac{-5i+5}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5-10i}{3-i}\frac{3+i}{3+i}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5-5i}{2}\cdot1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-5i+5}{2}\end{aligned} $$ | |
| ① | Divide $ \, 5-10i \, $ by $ \, 3-i \, $ to get $\,\, \dfrac{5-5i}{2} $. ( view steps )Divide $ \, 3+i \, $ by $ \, 3+i \, $ to get $\,\, 1 $. ( view steps ) |
| ② | Multiply $ \dfrac{5-5i}{2} $ by $ 1 $ to get $ \dfrac{-5i+5}{2} $. Step 1: Write $ 1 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{5-5i}{2} \cdot 1 & \xlongequal{\text{Step 1}} \frac{5-5i}{2} \cdot \frac{1}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 5-5i \right) \cdot 1 }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5-5i }{ 2 } = \frac{-5i+5}{2} \end{aligned} $$ |
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