Question
Answer
$$(12-9i)\cdot(12-9i)=81i^2-216i+144$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(12-9i)\cdot(12-9i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}144-108i-108i+81i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}81i^2-216i+144\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{12-9i}\right) $ by each term in $ \left( 12-9i\right) $. $$ \left( \color{blue}{12-9i}\right) \cdot \left( 12-9i\right) = 144-108i-108i+81i^2 $$ |
| ② | Combine like terms: $$ 144 \color{blue}{-108i} \color{blue}{-108i} +81i^2 = 81i^2 \color{blue}{-216i} +144 $$ |
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