Evaluate ( {f}ᵢ(0|j)|z) ), where ( {f}ᵢ(0|j) = e{-i{π}/{2}Jy/} ) is the operator that rotates kets counterclockwise by angle ( θ ) about the y-axis. Show that ( {f}₁({f}ⱼ)|z) = |x) ).
a) ( {f}ᵢ(0|j)|z) = e{-i{π}/{2}Jy/}|z) )
b) ( {f}ᵢ(0|j)|z) = e{i{π}/{2}Jy/}|z) )
c) ( {f}ᵢ(0|j)|z) = e{-i{π}/{2}Jₓ/}|z) )
d) ( {f}ᵢ(0|j)|z) = e{i{π}/{2}Jₓ/}|z) )