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