Question
Answer
$$-3i\cdot6i-3\cdot(-7+6i)=-18i+39$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-3i\cdot6i-3\cdot(-7+6i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-18i^2-3\cdot(-7+6i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}18-3\cdot(-7+6i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}18-(-21+18i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}18+21-18i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-18i+39\end{aligned} $$ | |
| ① | $$ 3 i \cdot 6 i = 18 i^{1 + 1} = 18 i^2 $$ |
| ② | $$ -18i^2 = -18 \cdot (-1) = 18 $$ |
| ③ | Multiply $ \color{blue}{3} $ by $ \left( -7+6i\right) $ $$ \color{blue}{3} \cdot \left( -7+6i\right) = -21+18i $$ |
| ④ | Remove the parentheses by changing the sign of each term within them. $$ - \left( -21+18i \right) = 21-18i $$ |
| ⑤ | Combine like terms: $$ \color{blue}{18} + \color{blue}{21} -18i = -18i+ \color{blue}{39} $$ |
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