Question
Answer
$$(40-9i)(a+7i)=-9ai+40a+280i+63$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(40-9i)(a+7i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}40a+280i-9ai-63i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}40a+280i-9ai-(-63) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-9ai+40a+280i+63\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{40-9i}\right) $ by each term in $ \left( a+7i\right) $. $$ \left( \color{blue}{40-9i}\right) \cdot \left( a+7i\right) = 40a+280i-9ai-63i^2 $$ |
| ② | $$ 63i^2 = 63 \cdot (-1) = -63 $$ |
| ③ | Combine like terms: $$ -9ai+40a+280i+63 = -9ai+40a+280i+63 $$ |
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