Question
Answer
$$5\cdot(2+i)+3i\cdot(4-2i)=17i+16$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5\cdot(2+i)+3i\cdot(4-2i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}10+5i+12i-6i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}10+5i+12i+6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}17i+16\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{5} $ by $ \left( 2+i\right) $ $$ \color{blue}{5} \cdot \left( 2+i\right) = 10+5i $$Multiply $ \color{blue}{3i} $ by $ \left( 4-2i\right) $ $$ \color{blue}{3i} \cdot \left( 4-2i\right) = 12i-6i^2 $$ |
| ② | $$ -6i^2 = -6 \cdot (-1) = 6 $$ |
| ③ | Combine like terms: $$ \color{blue}{10} + \color{red}{5i} + \color{red}{12i} + \color{blue}{6} = \color{red}{17i} + \color{blue}{16} $$ |
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