Question
Answer
$$(6-5i)\cdot(6+5i)=-25i^2+36$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(6-5i)\cdot(6+5i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}36+30i-30i-25i^2 \xlongequal{ } \\[1 em] & \xlongequal{ }36+ \cancel{30i} -\cancel{30i}-25i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-25i^2+36\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{6-5i}\right) $ by each term in $ \left( 6+5i\right) $. $$ \left( \color{blue}{6-5i}\right) \cdot \left( 6+5i\right) = 36+ \cancel{30i} -\cancel{30i}-25i^2 $$ |
| ② | Combine like terms: $$ 36+ \, \color{blue}{ \cancel{30i}} \, \, \color{blue}{ -\cancel{30i}} \,-25i^2 = -25i^2+36 $$ |
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