Question
Answer
$$(-2-2i)\cdot(-4-3i)\cdot(7+8i)=112i^2+114i+14$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-2-2i)\cdot(-4-3i)\cdot(7+8i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(8+6i+8i+6i^2)\cdot(7+8i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(6i^2+14i+8)\cdot(7+8i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(-6+14i+8)\cdot(7+8i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(14i+2)\cdot(7+8i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}98i+112i^2+14+16i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}112i^2+114i+14\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{-2-2i}\right) $ by each term in $ \left( -4-3i\right) $. $$ \left( \color{blue}{-2-2i}\right) \cdot \left( -4-3i\right) = 8+6i+8i+6i^2 $$ |
| ② | Combine like terms: $$ 8+ \color{blue}{6i} + \color{blue}{8i} +6i^2 = 6i^2+ \color{blue}{14i} +8 $$ |
| ③ | $$ 6i^2 = 6 \cdot (-1) = -6 $$ |
| ④ | Combine like terms: $$ \color{blue}{-6} +14i+ \color{blue}{8} = 14i+ \color{blue}{2} $$ |
| ⑤ | Multiply each term of $ \left( \color{blue}{14i+2}\right) $ by each term in $ \left( 7+8i\right) $. $$ \left( \color{blue}{14i+2}\right) \cdot \left( 7+8i\right) = 98i+112i^2+14+16i $$ |
| ⑥ | Combine like terms: $$ \color{blue}{98i} +112i^2+14+ \color{blue}{16i} = 112i^2+ \color{blue}{114i} +14 $$ |
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