Question
Answer
$$5\cdot(3-2i)+2i\cdot(4+6i)=-2i+3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5\cdot(3-2i)+2i\cdot(4+6i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}15-10i+8i+12i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}15-10i+8i-12 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-2i+3\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{5} $ by $ \left( 3-2i\right) $ $$ \color{blue}{5} \cdot \left( 3-2i\right) = 15-10i $$Multiply $ \color{blue}{2i} $ by $ \left( 4+6i\right) $ $$ \color{blue}{2i} \cdot \left( 4+6i\right) = 8i+12i^2 $$ |
| ② | $$ 12i^2 = 12 \cdot (-1) = -12 $$ |
| ③ | Combine like terms: $$ \color{blue}{15} \color{red}{-10i} + \color{red}{8i} \color{blue}{-12} = \color{red}{-2i} + \color{blue}{3} $$ |
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