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