Question
Answer
$$\dfrac{(a+bi)^2+1}{a+bi}=\dfrac{a^2+2abi+b^2i^2+1}{a+bi}$$
Explanation
| $$ \begin{aligned}\frac{(a+bi)^2+1}{a+bi}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{a^2+2abi+b^2i^2+1}{a+bi}\end{aligned} $$ | |
| 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 }$. $$ \begin{aligned}\left(a+bi\right)^2 = \color{blue}{a^2} +2 \cdot a \cdot bi + \color{red}{\left( bi \right)^2} = a^2+2abi+b^2i^2\end{aligned} $$ |
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