Question
Answer
$$(-i)^{13}=-i$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-i)^{13}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-i^{13} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-i\end{aligned} $$ | |
| ① | $$ \left( -i \right)^{13} = (-1)^{13}i^{13} = -i^{13} $$ |
| ② | $$ -i^{13} = - i^{4 \cdot 3 + 1} =
- \left( i^4 \right)^{ 3 } \cdot i^1 =
- 1^{ 3 } \cdot i =
- i $$ |
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