Question
Answer
$$(2+3i)x\cdot(2+3i)=9i^2x+12ix+4x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2+3i)x\cdot(2+3i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2x+3ix)\cdot(2+3i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4x+6ix+6ix+9i^2x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}9i^2x+12ix+4x\end{aligned} $$ | |
| ① | $$ \left( \color{blue}{2+3i}\right) \cdot x = 2x+3ix $$ |
| ② | Multiply each term of $ \left( \color{blue}{2x+3ix}\right) $ by each term in $ \left( 2+3i\right) $. $$ \left( \color{blue}{2x+3ix}\right) \cdot \left( 2+3i\right) = 4x+6ix+6ix+9i^2x $$ |
| ③ | Combine like terms: $$ 4x+ \color{blue}{6ix} + \color{blue}{6ix} +9i^2x = 9i^2x+ \color{blue}{12ix} +4x $$ |
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