Answer
$$(-8i)\cdot(2+5i)+4i\cdot(5+6i)=4i+16$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-8i)\cdot(2+5i)+4i\cdot(5+6i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-16i-40i^2+20i+24i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-16i+40+20i-24 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}4i+16\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{-8i} $ by $ \left( 2+5i\right) $ $$ \color{blue}{-8i} \cdot \left( 2+5i\right) = -16i-40i^2 $$Multiply $ \color{blue}{4i} $ by $ \left( 5+6i\right) $ $$ \color{blue}{4i} \cdot \left( 5+6i\right) = 20i+24i^2 $$ |
| ② | $$ -40i^2 = -40 \cdot (-1) = 40 $$$$ 24i^2 = 24 \cdot (-1) = -24 $$ |
| ③ | Combine like terms: $$ \color{blue}{-16i} + \color{red}{40} + \color{blue}{20i} \color{red}{-24} = \color{blue}{4i} + \color{red}{16} $$ |
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