Question
Answer
$$3i\cdot(5-4i)-(-12-8i)=23i+24$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3i\cdot(5-4i)-(-12-8i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}15i-12i^2-(-12-8i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}15i+12-(-12-8i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}15i+12+12+8i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}23i+24\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{3i} $ by $ \left( 5-4i\right) $ $$ \color{blue}{3i} \cdot \left( 5-4i\right) = 15i-12i^2 $$ |
| ② | $$ -12i^2 = -12 \cdot (-1) = 12 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( -12-8i \right) = 12+8i $$ |
| ④ | Combine like terms: $$ \color{blue}{15i} + \color{red}{12} + \color{red}{12} + \color{blue}{8i} = \color{blue}{23i} + \color{red}{24} $$ |
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