Answer
$$(6+7i)\cdot(6-7i)=-49i^2+36$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(6+7i)\cdot(6-7i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}36-42i+42i-49i^2 \xlongequal{ } \\[1 em] & \xlongequal{ }36 -\cancel{42i}+ \cancel{42i}-49i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-49i^2+36\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{6+7i}\right) $ by each term in $ \left( 6-7i\right) $. $$ \left( \color{blue}{6+7i}\right) \cdot \left( 6-7i\right) = 36 -\cancel{42i}+ \cancel{42i}-49i^2 $$ |
| ② | Combine like terms: $$ 36 \, \color{blue}{ -\cancel{42i}} \,+ \, \color{blue}{ \cancel{42i}} \,-49i^2 = -49i^2+36 $$ |
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