Question
Answer
$$(i-1)^2=-2i$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(i-1)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}i^2-2i+1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-1-2i+1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-2i\end{aligned} $$ | |
| ① | Find $ \left(i-1\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ i } $ and $ B = \color{red}{ 1 }$. $$ \begin{aligned}\left(i-1\right)^2 = \color{blue}{i^2} -2 \cdot i \cdot 1 + \color{red}{1^2} = i^2-2i+1\end{aligned} $$ |
| ② | $$ i^2 = -1 $$ |
| ③ | Combine like terms: $$ -2i \, \color{blue}{ -\cancel{1}} \,+ \, \color{blue}{ \cancel{1}} \, = -2i $$ |
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