Question
Answer
$$(-2i)\cdot(-3-4i)\cdot(-1-6i)=-36i^2+42i+8$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-2i)\cdot(-3-4i)\cdot(-1-6i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(6i+8i^2)\cdot(-1-6i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(6i-8)\cdot(-1-6i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-6i-36i^2+8+48i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-36i^2+42i+8\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{-2i} $ by $ \left( -3-4i\right) $ $$ \color{blue}{-2i} \cdot \left( -3-4i\right) = 6i+8i^2 $$ |
| ② | $$ 8i^2 = 8 \cdot (-1) = -8 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{6i-8}\right) $ by each term in $ \left( -1-6i\right) $. $$ \left( \color{blue}{6i-8}\right) \cdot \left( -1-6i\right) = -6i-36i^2+8+48i $$ |
| ④ | Combine like terms: $$ \color{blue}{-6i} -36i^2+8+ \color{blue}{48i} = -36i^2+ \color{blue}{42i} +8 $$ |
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