Question
Answer
$$i^{2024}-i^{2022}=1+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}i^{2024}-i^{2022}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}1+1\end{aligned} $$ | |
| ① | $$ i^{2024} = i^{4 \cdot 506 + 0} =
\left( i^4 \right)^{ 506 } \cdot i^0 =
1^{ 506 } \cdot 1 =
1 $$ |
| ② | $$ -i^{2022} = - i^{4 \cdot 505 + 2} =
- \left( i^4 \right)^{ 505 } \cdot i^2 =
- 1^{ 505 } \cdot (-1) =
- -1 = 1 $$ |
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