Question

复数z在复平面上对应的点在单位圆上,则复数(z方+1)/z

Answer 1

z=a+bi

在单位圆上

模等于1,所以a^2+b^2=1

(z^2+1)/z

=z^2/z+1/z

=z+1/z

=a+bi+1/(a+bi)

=a+bi+(a-bi)/(a+bi)(a-bi)

=a+bi+(a-bi)/(a^2+b^2)

=a+bi+(a-bi)/1

=2a

所以是实数,但不一定是0

所以选C