Question
Answer
$$20-8i\cdot(4+2i)=-32i+36$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}20-8i\cdot(4+2i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}20-(32i+16i^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}20-(32i-16) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}20-32i+16 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-32i+36\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{8i} $ by $ \left( 4+2i\right) $ $$ \color{blue}{8i} \cdot \left( 4+2i\right) = 32i+16i^2 $$ |
| ② | $$ 16i^2 = 16 \cdot (-1) = -16 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 32i-16 \right) = -32i+16 $$ |
| ④ | Combine like terms: $$ \color{blue}{20} -32i+ \color{blue}{16} = -32i+ \color{blue}{36} $$ |
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