若复数z满足|z|=1,求证z/1+z^2属于R
证明：
令z=cost+isint=(cost,sint)
z/1+z^2=cost+isint/1+cos^2t-sin^t+2sintcost=cost+isint/2cost+2isintcost=1/2cost∈R
z/1+z^2属于R 得证