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