If the square root of -1 is calculated to be i, and has merit due to its applications- why wouldn't the cube root of -1 be both -1 and an imaginary number?
Are there just no applications for it?
>>8178663
https://en.wikipedia.org/wiki/Root_of_unity
>>8178663
>why wouldn't the cube root of -1 be both -1 and an imaginary number?
Er, Why wouldn't there be two cube roots of -1: both -1, and an imaginary number?
>>8178663
0.5 + i*sqrt(3)/2
>>8178666
Actually... there are 3 cube roots of 1. Separated by 120 degrees in the complex plane.
>>8178665
Ok, so the only thing is that it states:
>Traditionally, z is assumed to be a complex number
and
>A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, that satisfies the equation i^2 = −1
What I'm talking about would be a 1/3 negative charge in the same sense that i is 1/2 a negative charge- and this appears to just loop back to i. I'll look through it closer...
>>8178668
>http://www.wolframalpha.com/input/?i=cube+roots+of+-1
-1, and two references to i...
What I'm saying is if i is essentially a 1/2 a negative charge, why isn't there an acute definition for a 1/3 negative charge?
Or can they always just be written in terms of i? (Which just doesn't sit well with me for some reason...)
>>8178680
>What I'm saying is if i is essentially a 1/2 a negative charge
No. For starters, what is -i?
>Or can they always just be written in terms of i?
Yes.
>(Which just doesn't sit well with me for some reason...)
If you want to add complexity to complex numbers, see quaternions, octonions, sedonions, as well as other variants such as split complex, split quaternions, ...
But the intuition you are attempting to apply is wrong. Learn more about complex numbers to get a better intuition, specifically multiplication and exponentiation as well as Euler's formula.
>>8178689
>No. For starters, what is -i?
-i = -sqrt(-1)
1/2 a negative charge isn't the correct term, i'll admit.
so is it just that charge is a value which is associated with any number ranging from positive to negative with numerical components in between?
Thats the only way I can think of i working as a factor of the cube root of -1...
So a charge can only be positive, negative, or i(or a multiple thereof)?
>>8178691
Hey anon, go get cucked (lol its funny because it implies you can get a woman) or something...
