Question
Answer
$$6i\cdot(1+i)-7\cdot(6-6i)=48i-48$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}6i\cdot(1+i)-7\cdot(6-6i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}6i+6i^2-(42-42i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6i-6-(42-42i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}6i-6-42+42i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}48i-48\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{6i} $ by $ \left( 1+i\right) $ $$ \color{blue}{6i} \cdot \left( 1+i\right) = 6i+6i^2 $$Multiply $ \color{blue}{7} $ by $ \left( 6-6i\right) $ $$ \color{blue}{7} \cdot \left( 6-6i\right) = 42-42i $$ |
| ② | $$ 6i^2 = 6 \cdot (-1) = -6 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 42-42i \right) = -42+42i $$ |
| ④ | Combine like terms: $$ \color{blue}{6i} \color{red}{-6} \color{red}{-42} + \color{blue}{42i} = \color{blue}{48i} \color{red}{-48} $$ |
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