Question
Answer
$$(13+7i)^2=182i+120$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(13+7i)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}169+182i+49i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}169+182i-49 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}182i+120\end{aligned} $$ | |
| ① | Find $ \left(13+7i\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 13 } $ and $ B = \color{red}{ 7i }$. $$ \begin{aligned}\left(13+7i\right)^2 = \color{blue}{13^2} +2 \cdot 13 \cdot 7i + \color{red}{\left( 7i \right)^2} = 169+182i+49i^2\end{aligned} $$ |
| ② | $$ 49i^2 = 49 \cdot (-1) = -49 $$ |
| ③ | Combine like terms: $$ 182i+ \color{blue}{169} \color{blue}{-49} = 182i+ \color{blue}{120} $$ |
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