Question
Answer
$$(0.4481+0.128i)^2-0.1+i=i$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(0.4481+0.128i)^2-0.1+i& \xlongequal{ }(0.4481+0i)^2-0.1+i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}0+0i+0i^2-0.1+i \xlongequal{ } \\[1 em] & \xlongequal{ } \cancel{0}0i0i^2 \cancel{0}+i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}i\end{aligned} $$ | |
| ① | Find $ \left(0+0i\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 0 } $ and $ B = \color{red}{ 0i }$. $$ \begin{aligned}\left(0+0i\right)^2 = \color{blue}{0^2} +2 \cdot 0 \cdot 0i + \color{red}{\left( 0i \right)^2} = 00i0i^2\end{aligned} $$ |
| ② | Combine like terms: $$ \, \color{blue}{ \cancel{0}} \, \color{green}{0i} 0i^2 \, \color{blue}{ \cancel{0}} \,+ \color{green}{i} = \color{green}{i} $$ |
This page was created using
Complex Expression calculator