Question
Answer
$$2\cdot(3+i)-3\cdot(-2-i)=5i+12$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2\cdot(3+i)-3\cdot(-2-i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}6+2i-(-6-3i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6+2i+6+3i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}5i+12\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2} $ by $ \left( 3+i\right) $ $$ \color{blue}{2} \cdot \left( 3+i\right) = 6+2i $$Multiply $ \color{blue}{3} $ by $ \left( -2-i\right) $ $$ \color{blue}{3} \cdot \left( -2-i\right) = -6-3i $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( -6-3i \right) = 6+3i $$ |
| ③ | Combine like terms: $$ \color{blue}{6} + \color{red}{2i} + \color{blue}{6} + \color{red}{3i} = \color{red}{5i} + \color{blue}{12} $$ |
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