Question
Answer
$$(5+3i)\cdot(2+9i)=27i^2+51i+10$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5+3i)\cdot(2+9i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}10+45i+6i+27i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}27i^2+51i+10\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{5+3i}\right) $ by each term in $ \left( 2+9i\right) $. $$ \left( \color{blue}{5+3i}\right) \cdot \left( 2+9i\right) = 10+45i+6i+27i^2 $$ |
| ② | Combine like terms: $$ 10+ \color{blue}{45i} + \color{blue}{6i} +27i^2 = 27i^2+ \color{blue}{51i} +10 $$ |
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