Answer
$$2\cdot(-36-3i)+(5+2i)\cdot(12-2i)=8i-8$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2\cdot(-36-3i)+(5+2i)\cdot(12-2i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-72-6i+60-10i+24i-4i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-72-6i-4i^2+14i+60 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-72-6i+4+14i+60 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-72-6i+14i+64 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}8i-8\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2} $ by $ \left( -36-3i\right) $ $$ \color{blue}{2} \cdot \left( -36-3i\right) = -72-6i $$ Multiply each term of $ \left( \color{blue}{5+2i}\right) $ by each term in $ \left( 12-2i\right) $. $$ \left( \color{blue}{5+2i}\right) \cdot \left( 12-2i\right) = 60-10i+24i-4i^2 $$ |
| ② | Combine like terms: $$ 60 \color{blue}{-10i} + \color{blue}{24i} -4i^2 = -4i^2+ \color{blue}{14i} +60 $$ |
| ③ | $$ -4i^2 = -4 \cdot (-1) = 4 $$ |
| ④ | Combine like terms: $$ \color{blue}{4} +14i+ \color{blue}{60} = 14i+ \color{blue}{64} $$ |
| ⑤ | Combine like terms: $$ \color{blue}{-72} \color{red}{-6i} + \color{red}{14i} + \color{blue}{64} = \color{red}{8i} \color{blue}{-8} $$ |
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