Question
Answer
$$(9-i)\cdot(9+i)=-i^2+81$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(9-i)\cdot(9+i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}81+9i-9i-i^2 \xlongequal{ } \\[1 em] & \xlongequal{ }81+ \cancel{9i} -\cancel{9i}-i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-i^2+81\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{9-i}\right) $ by each term in $ \left( 9+i\right) $. $$ \left( \color{blue}{9-i}\right) \cdot \left( 9+i\right) = 81+ \cancel{9i} -\cancel{9i}-i^2 $$ |
| ② | Combine like terms: $$ 81+ \, \color{blue}{ \cancel{9i}} \, \, \color{blue}{ -\cancel{9i}} \,-i^2 = -i^2+81 $$ |
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