Question
Answer
$$(3+i)(2-i+3i-4)=2i^2+4i-6$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3+i)(2-i+3i-4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(3+i)(2i-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6i-6+2i^2-2i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2i^2+4i-6\end{aligned} $$ | |
| ① | Combine like terms: $$ \color{blue}{2} \color{red}{-i} + \color{red}{3i} \color{blue}{-4} = \color{red}{2i} \color{blue}{-2} $$ |
| ② | Multiply each term of $ \left( \color{blue}{3+i}\right) $ by each term in $ \left( 2i-2\right) $. $$ \left( \color{blue}{3+i}\right) \cdot \left( 2i-2\right) = 6i-6+2i^2-2i $$ |
| ③ | Combine like terms: $$ \color{blue}{6i} -6+2i^2 \color{blue}{-2i} = 2i^2+ \color{blue}{4i} -6 $$ |
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