Question
Answer
$$(7-2i)\cdot(7+2i)=-4i^2+49$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(7-2i)\cdot(7+2i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}49+14i-14i-4i^2 \xlongequal{ } \\[1 em] & \xlongequal{ }49+ \cancel{14i} -\cancel{14i}-4i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-4i^2+49\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{7-2i}\right) $ by each term in $ \left( 7+2i\right) $. $$ \left( \color{blue}{7-2i}\right) \cdot \left( 7+2i\right) = 49+ \cancel{14i} -\cancel{14i}-4i^2 $$ |
| ② | Combine like terms: $$ 49+ \, \color{blue}{ \cancel{14i}} \, \, \color{blue}{ -\cancel{14i}} \,-4i^2 = -4i^2+49 $$ |
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