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This feels wrong. I love it.
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I think BAC is supposed to be defined as a right-angle, so that AB²+AC²=CB²
=> AB+1²=0²
=> AB = √-1
=> AB = i
I mean, I see that's how they would have had to get to i, but it's not a right triangle.
i is at a right angle (pi/2) to 1 by definition.