this post was submitted on 06 Nov 2023
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If I'm not wrong, I think the square root of minus 1 is an imaginary number which is represented by i
Don't ask me anymore questions about this if you want real answers because I genuinely don't know any more.
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
Powers of (1/√2 + i/√2) form a nice loop as well :)
Okay, that’s a deal. And thanks!