Complex Z / (1 + Z2) If the complex Z satisfies | Z | = 1, Z ≠ ± I, then Z / (1 + Z2) is () A real number B pure imaginary number C real number or pure imaginary number d imaginary number but not pure imaginary number

Complex Z / (1 + Z2) If the complex Z satisfies | Z | = 1, Z ≠ ± I, then Z / (1 + Z2) is () A real number B pure imaginary number C real number or pure imaginary number d imaginary number but not pure imaginary number

z=e^(iθ),θ≠(k+1/2)π
z/(1+z2)=1/[e^(iθ)+e^(-iθ)]=1/(2cosθ)
A real number