Question
Answer
$$-3\cdot(10+9i)+5i\cdot(-4-11i)=-47i+25$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-3\cdot(10+9i)+5i\cdot(-4-11i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-(30+27i)-20i-55i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-(30+27i)-20i+55 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-30-27i-20i+55 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-47i+25\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{3} $ by $ \left( 10+9i\right) $ $$ \color{blue}{3} \cdot \left( 10+9i\right) = 30+27i $$Multiply $ \color{blue}{5i} $ by $ \left( -4-11i\right) $ $$ \color{blue}{5i} \cdot \left( -4-11i\right) = -20i-55i^2 $$ |
| ② | $$ -55i^2 = -55 \cdot (-1) = 55 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left(30+27i \right) = -30-27i $$ |
| ④ | Combine like terms: $$ \color{blue}{-30} \color{red}{-27i} \color{red}{-20i} + \color{blue}{55} = \color{red}{-47i} + \color{blue}{25} $$ |
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