Question
Answer
$$1-\dfrac{i}{1}+i=1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}1-\frac{i}{1}+i& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{-i+1}{1}+i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{1}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}1\end{aligned} $$ | |
| ① | Subtract $ \dfrac{i}{1} $ from $ 1 $ to get $ \dfrac{-i+1}{1} $. Step 1: Write $ 1 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: To subtract expressions with the same denominators, we subtract the numerators and write the result over the common denominator. $$ \begin{aligned} 1- \frac{i}{1} & \xlongequal{\text{Step 1}} \frac{1}{\color{red}{1}} - \frac{i}{1} \xlongequal{\text{Step 2}} \frac{1}{\color{blue}{1}} - \frac{i}{\color{blue}{1}} = \\[1ex] &=\frac{ 1 - i }{ \color{blue}{ 1 }}= \frac{-i+1}{1} \end{aligned} $$ |
| ② | Add $ \dfrac{-i+1}{1} $ and $ i $ to get $ \dfrac{1}{1} $. Step 1: Write $ i $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: To add expressions with the same denominators, we add the numerators and write the result over the common denominator. $$ \begin{aligned} \frac{-i+1}{1} +i & \xlongequal{\text{Step 1}} \frac{-i+1}{1} + \frac{i}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{-i+1}{\color{blue}{1}} + \frac{i}{\color{blue}{1}} = \\[1ex] &=\frac{ -i+1 + i }{ \color{blue}{ 1 }}= \frac{1}{1} \end{aligned} $$ |
| ③ | Remove 1 from denominator. |
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