Answer
$$(5-2i)\cdot(4-i)=2i^2-13i+20$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5-2i)\cdot(4-i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}20-5i-8i+2i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2i^2-13i+20\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{5-2i}\right) $ by each term in $ \left( 4-i\right) $. $$ \left( \color{blue}{5-2i}\right) \cdot \left( 4-i\right) = 20-5i-8i+2i^2 $$ |
| ② | Combine like terms: $$ 20 \color{blue}{-5i} \color{blue}{-8i} +2i^2 = 2i^2 \color{blue}{-13i} +20 $$ |
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