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