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