Question
Answer
$$(1+2i)\cdot(1-4i)=-8i^2-2i+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(1+2i)\cdot(1-4i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}1-4i+2i-8i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-8i^2-2i+1\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{1+2i}\right) $ by each term in $ \left( 1-4i\right) $. $$ \left( \color{blue}{1+2i}\right) \cdot \left( 1-4i\right) = 1-4i+2i-8i^2 $$ |
| ② | Combine like terms: $$ 1 \color{blue}{-4i} + \color{blue}{2i} -8i^2 = -8i^2 \color{blue}{-2i} +1 $$ |
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