Answer
$$(5+2i)\cdot(-5-i)=-2i^2-15i-25$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5+2i)\cdot(-5-i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-25-5i-10i-2i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-2i^2-15i-25\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{5+2i}\right) $ by each term in $ \left( -5-i\right) $. $$ \left( \color{blue}{5+2i}\right) \cdot \left( -5-i\right) = -25-5i-10i-2i^2 $$ |
| ② | Combine like terms: $$ -25 \color{blue}{-5i} \color{blue}{-10i} -2i^2 = -2i^2 \color{blue}{-15i} -25 $$ |
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