Question
Answer
$$(125+125i)^2=31250i$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(125+125i)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}15625+31250i+15625i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}15625+31250i-15625 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}31250i\end{aligned} $$ | |
| ① | Find $ \left(125+125i\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 125 } $ and $ B = \color{red}{ 125i }$. $$ \begin{aligned}\left(125+125i\right)^2 = \color{blue}{125^2} +2 \cdot 125 \cdot 125i + \color{red}{\left( 125i \right)^2} = 15625+31250i+15625i^2\end{aligned} $$ |
| ② | $$ 15625i^2 = 15625 \cdot (-1) = -15625 $$ |
| ③ | Combine like terms: $$ 31250i+ \, \color{blue}{ \cancel{15625}} \, \, \color{blue}{ -\cancel{15625}} \, = 31250i $$ |
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