Question
Answer
$$1-2i+i^2\cdot(1-i)=-i$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}1-2i+i^2\cdot(1-i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}1-2i-1\cdot(1-i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}1-2i-1+i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-i\end{aligned} $$ | |
| ① | $$ i^2 = -1 $$ |
| ② | Multiply $ \color{blue}{-1} $ by $ \left( 1-i\right) $ $$ \color{blue}{-1} \cdot \left( 1-i\right) = -1+i $$ |
| ③ | Combine like terms: $$ \, \color{blue}{ \cancel{1}} \, \color{green}{-2i} \, \color{blue}{ -\cancel{1}} \,+ \color{green}{i} = \color{green}{-i} $$ |
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