Question
Answer
$$(-2+6i)^2=-24i-32$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-2+6i)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4-24i+36i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4-24i-36 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-24i-32\end{aligned} $$ | |
| ① | Find $ \left(-2+6i\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}{ 2 } $ and $ B = \color{red}{ 6i }$. $$ \begin{aligned}\left(-2+6i\right)^2& \xlongequal{ S1 } \left(2-6i\right)^2 \xlongequal{ S2 } \color{blue}{2^2} -2 \cdot 2 \cdot 6i + \color{red}{\left( 6i \right)^2} = \\[1 em] & = 4-24i+36i^2\end{aligned} $$ |
| ② | $$ 36i^2 = 36 \cdot (-1) = -36 $$ |
| ③ | Combine like terms: $$ -24i+ \color{blue}{4} \color{blue}{-36} = -24i \color{blue}{-32} $$ |
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