Let $\displaystyle z$ be a complex number represented by $\displaystyle x +iy $ What is the condition for the relationship between x and y such that $\displaystyle \frac {z}{1+z^2}$ is a real number? A. xy=1 B. x=y C. $\displaystyle x^2 -y^2 =1 $ D. $\displaystyle x^2 + y^2 =1 $ E. none of them above