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