Answer
$$(3-i)\cdot(4+5i)=-5i^2+11i+12$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3-i)\cdot(4+5i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}12+15i-4i-5i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-5i^2+11i+12\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{3-i}\right) $ by each term in $ \left( 4+5i\right) $. $$ \left( \color{blue}{3-i}\right) \cdot \left( 4+5i\right) = 12+15i-4i-5i^2 $$ |
| ② | Combine like terms: $$ 12+ \color{blue}{15i} \color{blue}{-4i} -5i^2 = -5i^2+ \color{blue}{11i} +12 $$ |
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