Question
Answer
$$(3+i)\cdot(2-i)+3i-4=2i+3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3+i)\cdot(2-i)+3i-4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}6-3i+2i-i^2+3i-4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-i^2-i+6+3i-4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}1-i+6+3i-4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-i+7+3i-4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}2i+3\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{3+i}\right) $ by each term in $ \left( 2-i\right) $. $$ \left( \color{blue}{3+i}\right) \cdot \left( 2-i\right) = 6-3i+2i-i^2 $$ |
| ② | Combine like terms: $$ 6 \color{blue}{-3i} + \color{blue}{2i} -i^2 = -i^2 \color{blue}{-i} +6 $$ |
| ③ | $$ -i^2 = -(-1) = 1 $$ |
| ④ | Combine like terms: $$ \color{blue}{1} -i+ \color{blue}{6} = -i+ \color{blue}{7} $$ |
| ⑤ | Combine like terms: $$ \color{blue}{-i} + \color{red}{7} + \color{blue}{3i} \color{red}{-4} = \color{blue}{2i} + \color{red}{3} $$ |
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