Answer
$$(-5+10i)\cdot(-5+10i)=100i^2-100i+25$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-5+10i)\cdot(-5+10i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}25-50i-50i+100i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}100i^2-100i+25\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{-5+10i}\right) $ by each term in $ \left( -5+10i\right) $. $$ \left( \color{blue}{-5+10i}\right) \cdot \left( -5+10i\right) = 25-50i-50i+100i^2 $$ |
| ② | Combine like terms: $$ 25 \color{blue}{-50i} \color{blue}{-50i} +100i^2 = 100i^2 \color{blue}{-100i} +25 $$ |
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