Answer
$$(-11-10i)^2=220i+21$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-11-10i)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}121+220i+100i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}121+220i-100 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}220i+21\end{aligned} $$ | |
| ① | Find $ \left(-11-10i\right)^2 $ in two steps. S1: Change all signs inside bracket. S2: Apply formula $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 11 } $ and $ B = \color{red}{ 10i }$. $$ \begin{aligned}\left(-11-10i\right)^2& \xlongequal{ S1 } \left(11+10i\right)^2 \xlongequal{ S2 } \color{blue}{11^2} +2 \cdot 11 \cdot 10i + \color{red}{\left( 10i \right)^2} = \\[1 em] & = 121+220i+100i^2\end{aligned} $$ |
| ② | $$ 100i^2 = 100 \cdot (-1) = -100 $$ |
| ③ | Combine like terms: $$ 220i+ \color{blue}{121} \color{blue}{-100} = 220i+ \color{blue}{21} $$ |
This page was created using
Complex Expression calculator