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