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Can |x| ever be negative in any case?

Mathematics
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nope
yes
|x| can't

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Other answers:

|i| is negative or positive
=1 is positive
Absolutely! My X is negative 50% of the time.
modulus i is positive
\[|\sqrt{-1}| = ?\] 0^2 + 1^2 = 1 ?
\[\text{magnitude of everything}\ge0\]
|(a+ib)^2| = a^2+b^2 ?
|a+ib|^2 = a^2+b^2
|a+ib| = sqrt(a^2+b^2)
Yep.. Thanks @mukushla and @Libniz and @hartnn
no problem
no because |x| = √(X² ) so even if you get any number + or - the number will be squared first making it to be + then it will be rooted to give you the number

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