Hello everyone I have to find the sum of all the square roots answers of the equation $(z + 1)^n = (z - 1)^n$.
I tried to use a = $z +1 , b = z -1$ and place $a^n - b^n = 0 = (a-b)(a^{n-1} + a^{n-2}b + ... + b^{n-1})$
And invert this to a polynomial and use Vieta's formula for finding the sum of all the square roots answers but I didn't success
someone can help me please?
Hint
Since $z\ne 1$ and $z\ne -1$, you can write $$({z+1\over z-1})^n=1$$hence all the roots of the equation can be obtained from $${z+1\over z-1}=e^{j{2\pi\over n}k}\quad,\quad k=0,1,\cdots n-1$$