Question
Answer
$$2(i^{21}+7)-(5-i^3)=i+9$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(i^{21}+7)-(5-i^3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2(1i+7)-(5+i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2i+14-(5+i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2i+14-5-i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}i+9\end{aligned} $$ | |
| ① | $$ i^{21} = i^{4 \cdot 5 + 1} =
\left( i^4 \right)^{ 5 } \cdot i^1 =
1^{ 5 } \cdot i =
i $$$$ -i^3 = - \color{blue}{i^2} \cdot i =
- ( \color{blue}{-1}) \cdot i =
\, i $$ |
| ② | Multiply $ \color{blue}{2} $ by $ \left( i+7\right) $ $$ \color{blue}{2} \cdot \left( i+7\right) = 2i+14 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 5+i \right) = -5-i $$ |
| ④ | Combine like terms: $$ \color{blue}{2i} + \color{red}{14} \color{red}{-5} \color{blue}{-i} = \color{blue}{i} + \color{red}{9} $$ |
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