Question
Answer
$$6\cdot(1-2i)+6i\cdot(-7+i)=-54i$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}6\cdot(1-2i)+6i\cdot(-7+i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}6-12i-42i+6i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6-12i-42i-6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-54i\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{6} $ by $ \left( 1-2i\right) $ $$ \color{blue}{6} \cdot \left( 1-2i\right) = 6-12i $$Multiply $ \color{blue}{6i} $ by $ \left( -7+i\right) $ $$ \color{blue}{6i} \cdot \left( -7+i\right) = -42i+6i^2 $$ |
| ② | $$ 6i^2 = 6 \cdot (-1) = -6 $$ |
| ③ | Combine like terms: $$ \, \color{blue}{ \cancel{6}} \, \color{green}{-12i} \color{green}{-42i} \, \color{blue}{ -\cancel{6}} \, = \color{green}{-54i} $$ |
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