设w=(-1/2)+(√3/2)i,集合M={z│z=w^n+w^(-n),n∈N},则M中元素有多少个?

由题知w=(-1/2)+(√3/2)i=cos(2π/3)+isin(2π/3)而z=w^n+w^(-n)=cos(2nπ/3)+isin(2nπ/3)+cos(-2nπ/3)+isin(-2nπ/3)=2cos(2nπ/3)其中,n∈Nn=3k(k∈N),z=2n=3k+1,3k+2(k∈N),z=-1综上,M中有2个元素...