Answer
$$(r+2-i)(r+2+i)=-i^2+r^2+4r+4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(r+2-i)(r+2+i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-i^2+r^2+4r+4\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{r+2-i}\right) $ by each term in $ \left( r+2+i\right) $. $$ \left( \color{blue}{r+2-i}\right) \cdot \left( r+2+i\right) = \\ = r^2+2r+ \cancel{ir}+2r+4+ \cancel{2i} -\cancel{ir} -\cancel{2i}-i^2 $$ |
| ② | Combine like terms: $$ r^2+ \color{blue}{2r} + \, \color{red}{ \cancel{ir}} \,+ \color{blue}{2r} +4+ \, \color{orange}{ \cancel{2i}} \, \, \color{red}{ -\cancel{ir}} \, \, \color{orange}{ -\cancel{2i}} \,-i^2 = -i^2+r^2+ \color{blue}{4r} +4 $$ |
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