Question
Answer
$$(3+10i)\cdot(3-10i)=-100i^2+9$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3+10i)\cdot(3-10i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}9-30i+30i-100i^2 \xlongequal{ } \\[1 em] & \xlongequal{ }9 -\cancel{30i}+ \cancel{30i}-100i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-100i^2+9\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{3+10i}\right) $ by each term in $ \left( 3-10i\right) $. $$ \left( \color{blue}{3+10i}\right) \cdot \left( 3-10i\right) = 9 -\cancel{30i}+ \cancel{30i}-100i^2 $$ |
| ② | Combine like terms: $$ 9 \, \color{blue}{ -\cancel{30i}} \,+ \, \color{blue}{ \cancel{30i}} \,-100i^2 = -100i^2+9 $$ |
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