Question
Answer
$$-i+7-5i-3\cdot(2-3i)=3i+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-i+7-5i-3\cdot(2-3i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-6i+7-3\cdot(2-3i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-6i+7-(6-9i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-6i+7-6+9i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}3i+1\end{aligned} $$ | |
| ① | Combine like terms: $$ \color{blue}{-i} +7 \color{blue}{-5i} = \color{blue}{-6i} +7 $$ |
| ② | Multiply $ \color{blue}{3} $ by $ \left( 2-3i\right) $ $$ \color{blue}{3} \cdot \left( 2-3i\right) = 6-9i $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 6-9i \right) = -6+9i $$ |
| ④ | Combine like terms: $$ \color{blue}{-6i} + \color{red}{7} \color{red}{-6} + \color{blue}{9i} = \color{blue}{3i} + \color{red}{1} $$ |
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