If z is a complex number satisfying z+(1/z)=1 calculate z^10+ (1/ z^10). Thanks in advance!

By the quadratic formula, z = sqrt(3)/2 + i/2, so z^10 + 1/z^10 = (sqrt(3)/2 + i/2)^10 + 1/(sqrt(3)/2 + i/2)^10 = 1.