The Powers of i
This video presents the same text shown beside it, spoken and on screen. It adds nothing the text does not say.
State
The powers of i cycle with period four: i, −1, −i, 1, then around again forever.
Show
i² = −1, i³ = i² · i = −i, i⁴ = (i²)² = 1, and i⁵ starts the wheel over at i. Any power reduces by remainders of four.
Builds on
- Nothing — this is a starting point.
Unlocks
- Nothing yet depends on this.