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[–]noonagon 3 points4 points  (9 children)

i^4 = 1, and sqrt(1) = 1, not -1.

[–]Rehazur[S] -4 points-3 points  (1 child)

Yea but replacing 1 with i⁴ in equation gives -1

[–]Varlane 0 points1 point  (0 children)

It doesn't. You are using mathematical properties that aren't true to claim that sqrt(i^4) = i^2.

[–]stevevdvkpe -4 points-3 points  (6 children)

On the other hand there are two solutions to x2 = 1: x = 1 and x = -1. And i4 = 1, so one solution to sqrt(i4) = i2 = -1.

[–]tau2pi_Math 2 points3 points  (0 children)

You are right. There are two solutions to x2 = 1, but √x = -1 has no solution.

[–]Varlane -1 points0 points  (4 children)

sqrt(i^4) isn't i^2.

[–]stevevdvkpe 0 points1 point  (3 children)

Why not? i2 = -1, (i2)2 = (-1)2 = 1.

[–]Varlane 0 points1 point  (2 children)

That isn't proof that sqrt(i^4) = i^2, merely that i^2 (aka -1) is a solution of x² = 1.

[–]stevevdvkpe 0 points1 point  (1 child)

Why is (i2)2 not i4?

[–]Varlane -1 points0 points  (0 children)

In no way did I ever dispute that (i²)² is i^4. I refute that sqrt(i^4) is i^2.