finestnothing, 1 year ago

Yep, sqrt(-1) = i. Powers of i are actually really neat imo since they form a loop: i^0 = 1
i^1 = i
i^2 = -1
i^3 (or i^2 x i or -1 x i) = -i
Now the loop starts:
i^4 = i^2 x i^2 = 1 x 1 = 1
i^5 = i^4 x i^1 = 1 x i = i
etc
Any evaluation of i to the power k boils down to i^(k%4). For example, i^726 = i^2 = -1. I know this was super useful in calc 1 or 2 and not used for any of my other math classes, it’s just a fun concept to me