I have always been annoyed by the statement that sqrt(-1) = i.
Note: I'm perfectly fine with the assertion that i^2 = -1.
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I have always been annoyed by the statement that sqrt(-1) = i.
Note: I'm perfectly fine with the assertion that i^2 = -1.
Jonathan Lamothe
in reply to Jonathan Lamothe • •sqrt(1) = -1. We're either constraining the answer to positive numbers or we're not.Pat
in reply to Jonathan Lamothe • • •piecewise function definitions are a thing though, like the abs function for instance
abs(x) = x, for all positive x
abs(x) = -x, for all negative x
sqrt(x) = positive y, for all positive x
sqrt(x) = i * sqrt(-x), for all negative x
I also find arctan really weird, because it only works if you fiddle with the domain (yet it clearly does exist, and is useful)
I enjoy the unpleasant feeling I get when I realise that all maths is made up!
Jonathan Lamothe
in reply to Pat • •abscan be defined for the whole complex plane though (the square root of the sum of the square of the real and imaginary components) i.e.:abs(a + bi) = sqrt(a^2 + b^2)Maddie
in reply to Jonathan Lamothe • • •Sensitive content
And with quaternions, we can pick any unit, like sqrt(-1) = (i+j+k)/sqrt(3)
y'know, where i = sqrt(-1), j = sqrt(-1), k = sqrt(-1) 😜
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