Question
Answer
$$(s-(-10+10i))(s-(-10-10i))=-100i^2+s^2+20s+100$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(s-(-10+10i))(s-(-10-10i))& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1s+10-10i)(1s+10+10i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-100i^2+s^2+20s+100\end{aligned} $$ | |
| ① | Remove the parentheses by changing the sign of each term within them. $$ - \left( -10+10i \right) = 10-10i $$Remove the parentheses by changing the sign of each term within them. $$ - \left( -10-10i \right) = 10+10i $$ |
| ② | Multiply each term of $ \left( \color{blue}{s+10-10i}\right) $ by each term in $ \left( s+10+10i\right) $. $$ \left( \color{blue}{s+10-10i}\right) \cdot \left( s+10+10i\right) = \\ = s^2+10s+ \cancel{10is}+10s+100+ \cancel{100i} -\cancel{10is} -\cancel{100i}-100i^2 $$ |
| ③ | Combine like terms: $$ s^2+ \color{blue}{10s} + \, \color{red}{ \cancel{10is}} \,+ \color{blue}{10s} +100+ \, \color{orange}{ \cancel{100i}} \, \, \color{red}{ -\cancel{10is}} \, \, \color{orange}{ -\cancel{100i}} \,-100i^2 = -100i^2+s^2+ \color{blue}{20s} +100 $$ |
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