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