Question
Answer
$$(1+3i)\dfrac{2-4i}{1+2i}=\dfrac{-26i+18}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(1+3i)\frac{2-4i}{1+2i}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1+3i)\frac{-6-8i}{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-24i^2-26i-6}{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{24-26i-6}{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-26i+18}{5}\end{aligned} $$ | |
| ① | Divide $ \, 2-4i \, $ by $ \, 1+2i \, $ to get $\,\, \dfrac{-6-8i}{5} $. ( view steps ) |
| ② | Multiply $1+3i$ by $ \dfrac{-6-8i}{5} $ to get $ \dfrac{-24i^2-26i-6}{5} $. Step 1: Write $ 1+3i $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 1+3i \cdot \frac{-6-8i}{5} & \xlongequal{\text{Step 1}} \frac{1+3i}{\color{red}{1}} \cdot \frac{-6-8i}{5} \xlongequal{\text{Step 2}} \frac{ \left( 1+3i \right) \cdot \left( -6-8i \right) }{ 1 \cdot 5 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -6-8i-18i-24i^2 }{ 5 } = \frac{-24i^2-26i-6}{5} \end{aligned} $$ |
| ③ | $$ -24i^2 = -24 \cdot (-1) = 24 $$ |
| ④ | Simplify numerator $$ \color{blue}{24} -26i \color{blue}{-6} = -26i+ \color{blue}{18} $$ |
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