Answer
$$(8-i)\cdot(5+3i)=-3i^2+19i+40$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(8-i)\cdot(5+3i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}40+24i-5i-3i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-3i^2+19i+40\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{8-i}\right) $ by each term in $ \left( 5+3i\right) $. $$ \left( \color{blue}{8-i}\right) \cdot \left( 5+3i\right) = 40+24i-5i-3i^2 $$ |
| ② | Combine like terms: $$ 40+ \color{blue}{24i} \color{blue}{-5i} -3i^2 = -3i^2+ \color{blue}{19i} +40 $$ |
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