Question
Answer
$$(5-4i)\cdot(2+7i)=-28i^2+27i+10$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5-4i)\cdot(2+7i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}10+35i-8i-28i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-28i^2+27i+10\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{5-4i}\right) $ by each term in $ \left( 2+7i\right) $. $$ \left( \color{blue}{5-4i}\right) \cdot \left( 2+7i\right) = 10+35i-8i-28i^2 $$ |
| ② | Combine like terms: $$ 10+ \color{blue}{35i} \color{blue}{-8i} -28i^2 = -28i^2+ \color{blue}{27i} +10 $$ |
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