Yes, it's , unless !
Hint : the sum of the roots of a polynomial is (up to sign) the coefficient of , and the roots of a complex number are the roots of .
Is there a theorem related to the sum of the roots of a positive number?
For example, for any integer n=1,2,3.....N, and positive number , such that are the nth roots of , what is the sum of the roots,
i.e. .
In other words, is there a closed form, and general solution for the sum of roots, i.e.
So, are you saying the sum of the roots of is 0 for n not equal 1, and, for n=1, the sum must be simply ? Thanks.. looking at the , I guess that makes sense.. I had long since forgotten, if I ever even knew it, that the sum of roots equals coefficient of Z in the polynomial.