Question
Answer
$$(5-3i)\cdot(5+3i)=-9i^2+25$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5-3i)\cdot(5+3i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}25+15i-15i-9i^2 \xlongequal{ } \\[1 em] & \xlongequal{ }25+ \cancel{15i} -\cancel{15i}-9i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-9i^2+25\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{5-3i}\right) $ by each term in $ \left( 5+3i\right) $. $$ \left( \color{blue}{5-3i}\right) \cdot \left( 5+3i\right) = 25+ \cancel{15i} -\cancel{15i}-9i^2 $$ |
| ② | Combine like terms: $$ 25+ \, \color{blue}{ \cancel{15i}} \, \, \color{blue}{ -\cancel{15i}} \,-9i^2 = -9i^2+25 $$ |
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