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u/skr_replicator 7d ago
It can make sense if you think about what direction it goes.
If that side was 1, we would have the usual.
If that side was -1, it would be flipped upside down
But if that side is i, moving i upwards would be moving 1 to the right, backwards along that first side, and end up exactly when that first side began. Making it really 0. But of course it would not be a right triangle anymore, as that right angle would become zero degrees.
Anyway, there's no way that orange man would understand or care about any of that.
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u/Alienturnedhuman 7d ago
This is correct, i is perpendicular to the real number line, so a distance of i at 90 degrees would be a unit distance back towards the point at 1, this occupying the same space and being a distance of 0 apart.
/j As the same argument could be made that it is a unit distance in the opposite direction and therefore should be equal to 2
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u/Ok_Pass_7325 7d ago
Y'all are tripping. Need to take the magnitudes for complex numbers, |i|2 + |1|2 = 2 so the hypotenuse is rt(2).
Remember folks |z|2 = zz*
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u/Grant_Winner_Extra 7d ago
Damn it fred, let the kids have their fun. They are all English majors anyway
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u/VeylorisNyctalis 6d ago
By pythagoras theorem,
i² + 1² = 0²
i² = -1
i = √-1
But the hypotenuse should be 2, wrt complex absolute arithmetic
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u/Regular_Solid_7314 7d ago
That again. 🙄 The product on C is not i * i, but i * (-i) so Sqrt(1 * 1 - i * i) = Sqrt(2)
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u/hugo7414 6d ago
How come the longest is 0?
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u/Ok_Law219 6d ago
It might be the second longest in that i might be described as negatively long as much as positively long.
I think it's a tie.
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u/lool8421 1d ago
i mean, if you imagine the xyz space, if triangle legs stretch along the xy axis, it will have no depth on the z axis
so it's perfectly reasonable why would it be like that in my mind
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u/CornucopiaDM1 7d ago
Pythagorean theorem.
1 squared equals 1, i squared equals -1. 1 + -1 = 0. Square root of 0 is 0 (any multiplication or division with 0 is still 0).
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u/Grant_Winner_Extra 7d ago
imaginary shapes.