Answer
$$(-8+i)^2=-16i+63$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-8+i)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}64-16i+i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}64-16i-1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-16i+63\end{aligned} $$ | |
| ① | Find $ \left(-8+i\right)^2 $ in two steps. S1: Change all signs inside bracket. S2: Apply formula $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 8 } $ and $ B = \color{red}{ i }$. $$ \begin{aligned}\left(-8+i\right)^2& \xlongequal{ S1 } \left(8-i\right)^2 \xlongequal{ S2 } \color{blue}{8^2} -2 \cdot 8 \cdot i + \color{red}{i^2} = \\[1 em] & = 64-16i+i^2\end{aligned} $$ |
| ② | $$ i^2 = -1 $$ |
| ③ | Combine like terms: $$ -16i+ \color{blue}{64} \color{blue}{-1} = -16i+ \color{blue}{63} $$ |
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