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