Question
Answer
$$(4-3i)\cdot(2+i)\cdot(-1+4i)=-8i^2+46i-11$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4-3i)\cdot(2+i)\cdot(-1+4i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(8+4i-6i-3i^2)\cdot(-1+4i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(-3i^2-2i+8)\cdot(-1+4i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(3-2i+8)\cdot(-1+4i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(-2i+11)\cdot(-1+4i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}2i-8i^2-11+44i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}-8i^2+46i-11\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{4-3i}\right) $ by each term in $ \left( 2+i\right) $. $$ \left( \color{blue}{4-3i}\right) \cdot \left( 2+i\right) = 8+4i-6i-3i^2 $$ |
| ② | Combine like terms: $$ 8+ \color{blue}{4i} \color{blue}{-6i} -3i^2 = -3i^2 \color{blue}{-2i} +8 $$ |
| ③ | $$ -3i^2 = -3 \cdot (-1) = 3 $$ |
| ④ | Combine like terms: $$ \color{blue}{3} -2i+ \color{blue}{8} = -2i+ \color{blue}{11} $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{-2i+11}\right) $ by each term in $ \left( -1+4i\right) $. $$ \left( \color{blue}{-2i+11}\right) \cdot \left( -1+4i\right) = 2i-8i^2-11+44i $$ |
| ⑥ | Combine like terms: $$ \color{blue}{2i} -8i^2-11+ \color{blue}{44i} = -8i^2+ \color{blue}{46i} -11 $$ |
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