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