Question
Answer
$$(z-(0.5+0.5i))(z-(0.5-0.5i))=z^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(z-(0.5+0.5i))(z-(0.5-0.5i))& \xlongequal{ }(z-(0.5+0i))(z-(0.5-0i)) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1z+0+0i)(1z+0+0i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}z^2\end{aligned} $$ | |
| ① | Remove the parentheses by changing the sign of each term within them. $$ - \left( 00i \right) = 00i $$Remove the parentheses by changing the sign of each term within them. $$ - \left( 00i \right) = 00i $$ |
| ② | Multiply each term of $ \left( \color{blue}{z00i}\right) $ by each term in $ \left( z00i\right) $. $$ \left( \color{blue}{z00i}\right) \cdot \left( z00i\right) = \\ = z^2 \cancel{0z} \cancel{0iz} \cancel{0z}0 \cancel{0i} \cancel{0iz} \cancel{0i}0i^2 $$ |
| ③ | Combine like terms: $$ z^2 \, \color{blue}{ \cancel{0z}} \, \, \color{green}{ \cancel{0iz}} \, \, \color{blue}{ \cancel{0z}} \,0 \, \color{blue}{ \cancel{0i}} \, \, \color{green}{ \cancel{0iz}} \, \, \color{blue}{ \cancel{0i}} \,0i^2 = z^2 $$ |
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