Question
Answer
$$(4-i)\cdot(5+2i)=-2i^2+3i+20$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4-i)\cdot(5+2i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}20+8i-5i-2i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-2i^2+3i+20\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{4-i}\right) $ by each term in $ \left( 5+2i\right) $. $$ \left( \color{blue}{4-i}\right) \cdot \left( 5+2i\right) = 20+8i-5i-2i^2 $$ |
| ② | Combine like terms: $$ 20+ \color{blue}{8i} \color{blue}{-5i} -2i^2 = -2i^2+ \color{blue}{3i} +20 $$ |
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