Answer
$$(-7-7i)^2=98i$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-7-7i)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}49+98i+49i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}49+98i-49 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}98i\end{aligned} $$ | |
| ① | Find $ \left(-7-7i\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}{ 7 } $ and $ B = \color{red}{ 7i }$. $$ \begin{aligned}\left(-7-7i\right)^2& \xlongequal{ S1 } \left(7+7i\right)^2 \xlongequal{ S2 } \color{blue}{7^2} +2 \cdot 7 \cdot 7i + \color{red}{\left( 7i \right)^2} = \\[1 em] & = 49+98i+49i^2\end{aligned} $$ |
| ② | $$ 49i^2 = 49 \cdot (-1) = -49 $$ |
| ③ | Combine like terms: $$ 98i+ \, \color{blue}{ \cancel{49}} \, \, \color{blue}{ -\cancel{49}} \, = 98i $$ |
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