Question
Answer
$$-i^{26}+i^{20}=1+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-i^{26}+i^{20}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}1+1\end{aligned} $$ | |
| ① | $$ -i^{26} = - i^{4 \cdot 6 + 2} =
- \left( i^4 \right)^{ 6 } \cdot i^2 =
- 1^{ 6 } \cdot (-1) =
- -1 = 1 $$ |
| ② | $$ i^{20} = i^{4 \cdot 5 + 0} =
\left( i^4 \right)^{ 5 } \cdot i^0 =
1^{ 5 } \cdot 1 =
1 $$ |
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