Answer
$$(3+4xi)^2=16i^2x^2+24ix+9$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3+4xi)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}9+24ix+16i^2x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}16i^2x^2+24ix+9\end{aligned} $$ | |
| ① | Find $ \left(3+4ix\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 3 } $ and $ B = \color{red}{ 4ix }$. $$ \begin{aligned}\left(3+4ix\right)^2 = \color{blue}{3^2} +2 \cdot 3 \cdot 4ix + \color{red}{\left( 4ix \right)^2} = 9+24ix+16i^2x^2\end{aligned} $$ |
| ② | Combine like terms: $$ 16i^2x^2+24ix+9 = 16i^2x^2+24ix+9 $$ |
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