Question
Answer
$$(10+10i)^2=200i$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(10+10i)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}100+200i+100i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}100+200i-100 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}200i\end{aligned} $$ | |
| ① | Find $ \left(10+10i\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 10 } $ and $ B = \color{red}{ 10i }$. $$ \begin{aligned}\left(10+10i\right)^2 = \color{blue}{10^2} +2 \cdot 10 \cdot 10i + \color{red}{\left( 10i \right)^2} = 100+200i+100i^2\end{aligned} $$ |
| ② | $$ 100i^2 = 100 \cdot (-1) = -100 $$ |
| ③ | Combine like terms: $$ 200i+ \, \color{blue}{ \cancel{100}} \, \, \color{blue}{ -\cancel{100}} \, = 200i $$ |
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