Question
Answer
$$(2+9i)^2=36i-77$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2+9i)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4+36i+81i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4+36i-81 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}36i-77\end{aligned} $$ | |
| ① | Find $ \left(2+9i\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 2 } $ and $ B = \color{red}{ 9i }$. $$ \begin{aligned}\left(2+9i\right)^2 = \color{blue}{2^2} +2 \cdot 2 \cdot 9i + \color{red}{\left( 9i \right)^2} = 4+36i+81i^2\end{aligned} $$ |
| ② | $$ 81i^2 = 81 \cdot (-1) = -81 $$ |
| ③ | Combine like terms: $$ 36i+ \color{blue}{4} \color{blue}{-81} = 36i \color{blue}{-77} $$ |
This page was created using
Complex Expression calculator