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