Question
Answer
$$(6+i)\cdot(-3+2i)\cdot(-2)\cdot(1+2i)=-36i^2+62i+40$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(6+i)\cdot(-3+2i)\cdot(-2)\cdot(1+2i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(-18+12i-3i+2i^2)\cdot(-2)\cdot(1+2i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(2i^2+9i-18)\cdot(-2)\cdot(1+2i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(-2+9i-18)\cdot(-2)\cdot(1+2i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(9i-20)\cdot(-2)\cdot(1+2i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}(-18i+40)\cdot(1+2i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}-18i-36i^2+40+80i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}-36i^2+62i+40\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{6+i}\right) $ by each term in $ \left( -3+2i\right) $. $$ \left( \color{blue}{6+i}\right) \cdot \left( -3+2i\right) = -18+12i-3i+2i^2 $$ |
| ② | Combine like terms: $$ -18+ \color{blue}{12i} \color{blue}{-3i} +2i^2 = 2i^2+ \color{blue}{9i} -18 $$ |
| ③ | $$ 2i^2 = 2 \cdot (-1) = -2 $$ |
| ④ | Combine like terms: $$ \color{blue}{-2} +9i \color{blue}{-18} = 9i \color{blue}{-20} $$ |
| ⑤ | $$ \left( \color{blue}{9i-20}\right) \cdot -2 = -18i+40 $$ |
| ⑥ | Multiply each term of $ \left( \color{blue}{-18i+40}\right) $ by each term in $ \left( 1+2i\right) $. $$ \left( \color{blue}{-18i+40}\right) \cdot \left( 1+2i\right) = -18i-36i^2+40+80i $$ |
| ⑦ | Combine like terms: $$ \color{blue}{-18i} -36i^2+40+ \color{blue}{80i} = -36i^2+ \color{blue}{62i} +40 $$ |
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