Question
Answer
$$(3-7i)\cdot(7+8i)+7+6i-8+2i=-17i+76$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3-7i)\cdot(7+8i)+7+6i-8+2i& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}21+24i-49i-56i^2+7+6i-8+2i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-56i^2-25i+21+7+6i-8+2i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}56-25i+21+7+6i-8+2i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-25i+77+7+6i-8+2i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-19i+84-8+2i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}-17i+76\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{3-7i}\right) $ by each term in $ \left( 7+8i\right) $. $$ \left( \color{blue}{3-7i}\right) \cdot \left( 7+8i\right) = 21+24i-49i-56i^2 $$ |
| ② | Combine like terms: $$ 21+ \color{blue}{24i} \color{blue}{-49i} -56i^2 = -56i^2 \color{blue}{-25i} +21 $$ |
| ③ | $$ -56i^2 = -56 \cdot (-1) = 56 $$ |
| ④ | Combine like terms: $$ \color{blue}{56} -25i+ \color{blue}{21} = -25i+ \color{blue}{77} $$ |
| ⑤ | Combine like terms: $$ \color{blue}{-25i} + \color{red}{77} + \color{red}{7} + \color{blue}{6i} = \color{blue}{-19i} + \color{red}{84} $$ |
| ⑥ | Combine like terms: $$ \color{blue}{-19i} + \color{red}{84} \color{red}{-8} + \color{blue}{2i} = \color{blue}{-17i} + \color{red}{76} $$ |
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