Answer
$$(-2+4i)\cdot(5+i)=4i^2+18i-10$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-2+4i)\cdot(5+i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-10-2i+20i+4i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4i^2+18i-10\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{-2+4i}\right) $ by each term in $ \left( 5+i\right) $. $$ \left( \color{blue}{-2+4i}\right) \cdot \left( 5+i\right) = -10-2i+20i+4i^2 $$ |
| ② | Combine like terms: $$ -10 \color{blue}{-2i} + \color{blue}{20i} +4i^2 = 4i^2+ \color{blue}{18i} -10 $$ |
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