Question
Answer
$$3\cdot(7-3i)+i\cdot(2+2i)=-7i+19$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3\cdot(7-3i)+i\cdot(2+2i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}21-9i+2i+2i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}21-9i+2i-2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-7i+19\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{3} $ by $ \left( 7-3i\right) $ $$ \color{blue}{3} \cdot \left( 7-3i\right) = 21-9i $$Multiply $ \color{blue}{i} $ by $ \left( 2+2i\right) $ $$ \color{blue}{i} \cdot \left( 2+2i\right) = 2i+2i^2 $$ |
| ② | $$ 2i^2 = 2 \cdot (-1) = -2 $$ |
| ③ | Combine like terms: $$ \color{blue}{21} \color{red}{-9i} + \color{red}{2i} \color{blue}{-2} = \color{red}{-7i} + \color{blue}{19} $$ |
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