Question
Answer
$$(-3+2i)\cdot(-3-2i)=-4i^2+9$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-3+2i)\cdot(-3-2i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}9+6i-6i-4i^2 \xlongequal{ } \\[1 em] & \xlongequal{ }9+ \cancel{6i} -\cancel{6i}-4i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-4i^2+9\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{-3+2i}\right) $ by each term in $ \left( -3-2i\right) $. $$ \left( \color{blue}{-3+2i}\right) \cdot \left( -3-2i\right) = 9+ \cancel{6i} -\cancel{6i}-4i^2 $$ |
| ② | Combine like terms: $$ 9+ \, \color{blue}{ \cancel{6i}} \, \, \color{blue}{ -\cancel{6i}} \,-4i^2 = -4i^2+9 $$ |
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