Question
Answer
$$(-i)^{12}=1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-i)^{12}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}i^{12} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}1\end{aligned} $$ | |
| ① | $$ \left( -i \right)^{12} = (-1)^{12}i^{12} = i^{12} $$ |
| ② | $$ i^{12} = i^{4 \cdot 3 + 0} =
\left( i^4 \right)^{ 3 } \cdot i^0 =
1^{ 3 } \cdot 1 =
1 $$ |
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