Complex solutions of $(x+1)^{10}+(x-1)^{10}=0$ Solve $$(x+1)^{10}+(x-1)^{10}=0$$
What method is available to solve this equation?

As pointed out by Gerry Myerson's comment , put $\frac{x+1}{x-1}=z$ for some complex $z,x\neq1$ Then, $x=\frac{z+1}{z-1}$. Now your equation reduces to $z^{10}=-1$, which is easily solvable by using Euler's/De-Moivre's Theorem as $z=e^{i\phi},\phi=\frac{(2k+1)\pi}{10},k\in\mathbb{Z^+\cup 0}:k<10$ from which $x$ can be calculated
