Answer
$$(7+3i)^2=42i+40$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(7+3i)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}49+42i+9i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}49+42i-9 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}42i+40\end{aligned} $$ | |
| ① | Find $ \left(7+3i\right)^2 $ using 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}{ 3i }$. $$ \begin{aligned}\left(7+3i\right)^2 = \color{blue}{7^2} +2 \cdot 7 \cdot 3i + \color{red}{\left( 3i \right)^2} = 49+42i+9i^2\end{aligned} $$ |
| ② | $$ 9i^2 = 9 \cdot (-1) = -9 $$ |
| ③ | Combine like terms: $$ 42i+ \color{blue}{49} \color{blue}{-9} = 42i+ \color{blue}{40} $$ |
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