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Why is i^4 equal to 1? I keep confusing the powers of i.

RVRohit Verma · 10 Asked 14d ago 144 views 1 answer

I know i = sqrt(-1) but I always mess up the cycle of powers. Is there a shortcut to find i^n for any large n like i^237?

1 Answer

ARAnanya Reddy ✓ Accepted · 14d ago ▲ 3

The powers of i cycle with period 4: i^1=i, i^2=-1, i^3=-i, i^4=1, i^5=i... For i^n, divide n by 4 and use the remainder. i^237: 237 = 4*59 + 1, so remainder is 1, meaning i^237 = i^1 = i. The rule: r=0 gives 1, r=1 gives i, r=2 gives -1, r=3 gives -i.

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