Answer
$$(x+0.5+i\cdot0.8)(x+0.5-i\cdot0.8)(s+1)=sx^2+x^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+0.5+i\cdot0.8)(x+0.5-i\cdot0.8)(s+1)& \xlongequal{ }(x+0.5+0i)(x+0.5-0i)(s+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^2(s+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}sx^2+x^2\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x00i}\right) $ by each term in $ \left( x00i\right) $. $$ \left( \color{blue}{x00i}\right) \cdot \left( x00i\right) = \\ = x^2 \cancel{0x} \cancel{0ix} \cancel{0x}0 \cancel{0i} \cancel{0ix} \cancel{0i}0i^2 $$ |
| ② | Combine like terms: $$ x^2 \, \color{blue}{ \cancel{0x}} \, \, \color{green}{ \cancel{0ix}} \, \, \color{blue}{ \cancel{0x}} \,0 \, \color{blue}{ \cancel{0i}} \, \, \color{green}{ \cancel{0ix}} \, \, \color{blue}{ \cancel{0i}} \,0i^2 = x^2 $$ |
| ③ | Multiply $ \color{blue}{x^2} $ by $ \left( s+1\right) $ $$ \color{blue}{x^2} \cdot \left( s+1\right) = sx^2+x^2 $$ |
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