Question
Answer
$$(5-5i)^2=-50i$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5-5i)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}25-50i+25i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}25-50i-25 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-50i\end{aligned} $$ | |
| ① | Find $ \left(5-5i\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 5 } $ and $ B = \color{red}{ 5i }$. $$ \begin{aligned}\left(5-5i\right)^2 = \color{blue}{5^2} -2 \cdot 5 \cdot 5i + \color{red}{\left( 5i \right)^2} = 25-50i+25i^2\end{aligned} $$ |
| ② | $$ 25i^2 = 25 \cdot (-1) = -25 $$ |
| ③ | Combine like terms: $$ -50i+ \, \color{blue}{ \cancel{25}} \, \, \color{blue}{ -\cancel{25}} \, = -50i $$ |
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