Question

设z是虚数,w=z+1/z是实数,且-1

Answer 1

1、设z=x+yi(x、y∈R,y≠0),w=x+yi+1/(x+yi)=x+x/(x²+y²)+[y-y/(x²+y²)]i

由w是实数,得y-y/(x²+y²=0,由y≠0得x²+y²=1.

所以|z|=1.

于是w=2x,所以-1