Question
Answer
$$4\cdot(3-5i)-2i\cdot(-8+5i)=-4i+22$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4\cdot(3-5i)-2i\cdot(-8+5i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}12-20i-(-16i+10i^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}12-20i-(-16i-10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}12-20i+16i+10 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-4i+22\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{4} $ by $ \left( 3-5i\right) $ $$ \color{blue}{4} \cdot \left( 3-5i\right) = 12-20i $$Multiply $ \color{blue}{2i} $ by $ \left( -8+5i\right) $ $$ \color{blue}{2i} \cdot \left( -8+5i\right) = -16i+10i^2 $$ |
| ② | $$ 10i^2 = 10 \cdot (-1) = -10 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( -16i-10 \right) = 16i+10 $$ |
| ④ | Combine like terms: $$ \color{blue}{12} \color{red}{-20i} + \color{red}{16i} + \color{blue}{10} = \color{red}{-4i} + \color{blue}{22} $$ |
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