Answer
$$(-8-9i)^2=144i-17$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-8-9i)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}64+144i+81i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}64+144i-81 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}144i-17\end{aligned} $$ | |
| ① | Find $ \left(-8-9i\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}{ 9i }$. $$ \begin{aligned}\left(-8-9i\right)^2& \xlongequal{ S1 } \left(8+9i\right)^2 \xlongequal{ S2 } \color{blue}{8^2} +2 \cdot 8 \cdot 9i + \color{red}{\left( 9i \right)^2} = \\[1 em] & = 64+144i+81i^2\end{aligned} $$ |
| ② | $$ 81i^2 = 81 \cdot (-1) = -81 $$ |
| ③ | Combine like terms: $$ 144i+ \color{blue}{64} \color{blue}{-81} = 144i \color{blue}{-17} $$ |
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