Question
Answer
$$(a+bi)(c+di)=bdi^2+adi+bci+ac$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(a+bi)(c+di)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}ac+adi+bci+bdi^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}bdi^2+adi+bci+ac\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{a+bi}\right) $ by each term in $ \left( c+di\right) $. $$ \left( \color{blue}{a+bi}\right) \cdot \left( c+di\right) = ac+adi+bci+bdi^2 $$ |
| ② | Combine like terms: $$ bdi^2+adi+bci+ac = bdi^2+adi+bci+ac $$ |
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