Question
Answer
$$(4-5i)\cdot(4-5i)=25i^2-40i+16$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4-5i)\cdot(4-5i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}16-20i-20i+25i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}25i^2-40i+16\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{4-5i}\right) $ by each term in $ \left( 4-5i\right) $. $$ \left( \color{blue}{4-5i}\right) \cdot \left( 4-5i\right) = 16-20i-20i+25i^2 $$ |
| ② | Combine like terms: $$ 16 \color{blue}{-20i} \color{blue}{-20i} +25i^2 = 25i^2 \color{blue}{-40i} +16 $$ |
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