Question
Answer
$$(10+4i)\cdot(10-4i)=-16i^2+100$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(10+4i)\cdot(10-4i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}100-40i+40i-16i^2 \xlongequal{ } \\[1 em] & \xlongequal{ }100 -\cancel{40i}+ \cancel{40i}-16i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-16i^2+100\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{10+4i}\right) $ by each term in $ \left( 10-4i\right) $. $$ \left( \color{blue}{10+4i}\right) \cdot \left( 10-4i\right) = 100 -\cancel{40i}+ \cancel{40i}-16i^2 $$ |
| ② | Combine like terms: $$ 100 \, \color{blue}{ -\cancel{40i}} \,+ \, \color{blue}{ \cancel{40i}} \,-16i^2 = -16i^2+100 $$ |
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